ecessit 


iliiornia 

jLoiial 

ility 


IclUUe 


LIBRARY  OF 

ARCHITECTURE  AND 

ALLIED  ARTS 


Gift  of 

The  Heirs 
of 
R,  Germain  Hubby,  A. I. A. 


Digitized  by  the  Internet  Arciiive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/beautifulnecessiOObragiala 


THE  BEAUTIFUL 
NECESSITY 


THE  BEAUTIFUL 
NECESSITY 

Seven  Essays  on 
Theosophy  and  Architecture 


h 
Claude  Bragdon 


ROCHESTER,  N.  Y. 

THE   MANAS   PRESS 

I  910 


Copyright  igio 
by 

Claude  Bragdon 


*j!*«tectuni  ft 
Urban  Planning 

AJA 


"Let  us  build  altars  to  the  Beautiful  Necessity" 

— Emerson 


CONTENTS 

I 

The  Theosophic  View  of  the  Art  of  Architecture       9-21 

II 
Unity  AND  Polarity        .         .         .         .         .         .22-32 

III 
Changeless  Change  .         .         .         .         .         '33-49 

IV 
The  Bodily  Temple         .         .         .         .         .         '50-59 

V 
Latent  Geometry  .         .         .         .         .         .60-75 

VI 
The  Arithmetic  OF  Beauty     .         .         .         .         .76-84 

VII 
Frozen  Music  .         .         .         .         .         .         .85-92 

Conclusion       ........  93 


THE  THEOSOPHIC  VIEW  OF  THE 
ART  OF  ARCHITECTURE 

ONE  of  the  many  advantages  of  a  thorough  assimilation  of  what  may 
be  called  the  theosophic  idea  is  that  it  can  be  applied  with  advantage 
to  every  department  of  knowledge  and  of  human  activity:  like  the 
key  to  a  cryptogram,  it  renders  clear  and  simple  that  which  before  was  in- 
tricate and  obscure.  Let  us  apply  this  key  to  the  subject  of  art,  and  to  the 
art  of  architecture  in  particular,  and  let  us  see  if  by  so  doing  we  may  not 
learn  more  of  art  than  we  knew  before,  and  more  of  theosophy,  too. 

The  theosophic  idea  is  that  everything  is  an  expression  of  the  Self, — or 
whatever  other  name  one  may  choose  to  give  to  that  immanent  unknown 
reality  which  forever  hides  behind  all  phenomenal  life, — but  because  on  the 
physical  plane  our  only  avenue  of  knowledge  is  sense  perception,  a  more 
exact  expression  of  the  theosophic  idea  would  be:  Everything  is  the  ex- 
pression of  the  Self  in  terms  of  sense.  Art,  accordingly,  is  the  expression  of 
the  Self  in  terms  of  sense.  Now,  though  the  Self  is  one,  sense  is  not  one,  but 
manifold,  and  so  there  are  arts,  each  addressed  to  some  particular  faculty  or 
group  of  faculties,  and  each  expressing  some  particular  quality  or  group  of 
qualities  of  the  Self.  The  white  light  of  Truth  is  thus  broken  up  into  a  rain- 
bow-tinted spectrum  of  Beauty,  in  which  the  various  arts  are  colors,  each 
distinct,  yet  merging  one  into  another, — poetry  into  music;  painting  into 
decoration ;  decoration  becoming  sculpture ;  sculpture,  architecture,  and  so  on. 

In  such  a  spectrum  of  the  arts  each  one  occupies  a  definite  place,  and 
all  together  form  a  series  of  which  music  and  architecture  are  the  two  ex- 
tremes.   That  such  is  their  relative  position  may  be  demonstrated  in  various 

[9] 


lO  THE  BEAUTIFUL  NECESSITY  i 

ways:  the  theosophic  explanation  involving  the  familiar  idea  of  the  "pairs 
of  opposites"  would  be  something  as  follows :  According  to  the  Hindu-Aryan 
theory,  Brahma,  that  the  world  .might  be  born,  fell  asunder  into  man  and 
wife,  became  in  other  words,  name  and  form.*  The  two  universal  aspects  of 
name  and  form  are  what  philosophers  call  the  two  "modes  of  consciousness," 
one  of  time,  and  the  other  of  space.  These  are  the  two  gates  through  which 
ideas  enter  phenomenal  life:  the  two  boxes,  as  it  were,  that  contain  all  the 
toys  with  which  we  play.  Everything,  if  we  were  only  keen  enough  to  per- 
ceive it,  bears  the  mark  of  one  or  the  other  of  them,  and  may  be  classified 
accordingly.  In  such  a  classification  music  is  seen  to  be  allied  to  time,  and 
architecture  to  space,  because  music  is  successive  in  its  mode  of  manifesta- 
tion, and  in  time  alone  everything  would  occur  successively,  one  thing  follow- 
ing another ;  while  architecture,  on  the  other  hand,  impresses  itself  upon  the 
beholder  all  at  once,  and  in  space  alone  all  things  would  exist  simultaneously. 
Music,  which  is  in  time  alone,  without  any  relation  to  space,  and  architecture, 
which  is  in  space  alone,  without  any  relation  to  time,  are  thus  seen  to  stand  at 
opposite  ends  of  the  art  spectrum,  and  to  be,  in  a  sense,  the  only  "pure"  arts, 
because  in  all  the  others  the  elements  of  both  time  and  space  enter  in  varying 
proportions,  either  actually  or  by  implication.  Poetry  and  the  drama  are 
allied  to  music  insomuch  as  the  ideas  and  images  of  which  they  are  made  up 
are  presented  successively,  yet  these  images  are,  for  the  most  part,  forms 
of  space.  Sculpture,  on  the  other  hand,  is  clearly  allied  to  architecture,  and 
so  to  space,  but  the  element  of  action,  suspended  though  it  be,  affiliates  it  with 
the  opposite,  or  time  pole.  Painting  occupies  a  middle  position,  since  in  it 
space  instead  of  being  actual  has  become  ideal, — three  dimensions  being  ex- 
pressed through  the  mediumship  of  two, — and  time  enters  into  it  more  largely 
than  into  sculpture  by  reason  of  the  greater  ease  with  which  complicated 
action  can  be  indicated :  a  picture  being  nearly  always  time  arrested  in  mid- 
course,  a  moment  transfixed. 

In  order  to  form  a  just  conception  of  the  relation  between  music  and 
architecture  it  is  necessary  that  the  two  should  be  conceived  of,  not  as  standing 
at  opposite  ends  of  a  series  represented  by  a  straight  line,  but  rather  in 

♦The  quaint  Oriental  imagery  here  employed  should  not  blind  the  reader  to  the 
precise  scientific  accuracy  of  the  idea  of  which  this  imagery  is  the  vehicle.  Schopen- 
hauer says :  "Polarity,  or  the  sundering  of  a  force  into  two  quantitatively  different  and 
opposed  activities,  striving  after  re-union,  ...  is  a  fundamental  type  of  almost  all 
the  phenomena  of  nature,  from  the  magnet  and  the  crystal  to  man  himself." 


I  THE  ART  OF  ARCHITECTURE  ii 

juxtaposition,  as  in  the  ancient  Egyptian  symbol  of  a  serpent  holding  its  tail 
in  its  mouth,  the  head  in  this  case  corresponding  to  music,  and  the  tail  to 
architecture;  in  other  words,  though  in  one  sense  they  are  the  most  widely 
separated  of  the  arts,  in  another  they  are  the  most  closely  related. 

Music  being  purely  in  time  and  architecture  being  purely  in  space,  each 
is,  in  a  manner,  and  to  a  degree  not  possible  with  any  of  the  other  arts,  con- 
vertible into  the  other,  by  reason  of  the  correspondence  subsisting  between 
intervals  of  time  and  intervals  of  space.  A  perception  of  this  may  have 
inspired  the  famous  saying  that  architecture  is  frozen  music,  a  poetical  state- 
ment of  a  philosophical  truth,  since  that  which  in  music  is  expressed  by  means 
of  harmonious  intervals  of  time  and  pitch,  successively,  after  the  manner  of 
time,  may  be  translated  into  corresponding  intervals  of  architectural  void  and 
solid,  height  and  width. 

In  another  sense  music  and  architecture  are  allied.  They  alone  of  all  the 
arts  are  purely  creative,  since  in  them  is  presented,  not  a  likeness  of  some 
known  idea,  but  a  thing-in-itself  brought  to  a  distinct  and  complete  expres- 
sion of  its  nature.  Neither  a  musical  composition  nor  a  work  of  architecture 
depends  for  its  effectiveness  upon  resemblances  to  natural  sounds  in  the 
one  case,  or  to  natural  forms  in  the  other.  Of  none  of  the  other  arts  is  this 
to  such  a  degree  true :  they  are  not  so  much  creative  as  re-creative,  for  in 
them  all  the  artist  takes  his  subject  ready  made  from  nature  and  presents  it 
anew  according  to  the  dictates  of  his  genius. 

The  characteristic  differences  between  music  and  architecture  are  the 
same  as  those  which  subsist  between  time  and  space.  Now  time  and  space 
are  such  abstract  ideas  that  they  can  be  best  understood  through  their  cor- 
responding correlatives  in  the  natural  world,  for  it  is  a  fundamental  theo- 
sophic  tenet  that  nature  everywhere  abounds  in  such  correspondences;  that 
nature,  in  its  myriad  forms,  is  indeed  the  concrete  presentment  of  abstract 
unities.  The  energy  which  everywhere  informs  matter  is  a  type  of  time 
within  space ;  the  mind  working  in  and  through  the  body  is  another  expres- 
sion of  the  same  thing.  Accordingly,  music  is  dynamic,  subjective,  mental, 
of  one  dimension;  while  architecture  is  static,  objective,  physical,  of  three 
dimensions ;  sustaining  the  same  relation  to  music  and  the  other  arts  as  does 
the  human  body  to  the  various  organs  which  compose,  and  consciousnesses 
which  animate  it,  (it  being  the  reservatory  of  these  organs  and  the  vehicle 
of  these  consciousnesses);  and  a  work  of  architecture,  in  like  manner,  may, 
and  sometimes  does  include  all  of  the  other  arts  within  itself.     Sculpture 


12  THE  BEAUTIFUL  NECESSITY  "  i 

accentuates  and  enriches,  painting  adorns  it,  works  of  literature  are  stored 
within  it,  poetry  and  the  drama  awake  its  echoes,  while  music  thrills  to  its 
uttermost  recesses,  like  the  very  spirit  of  life  tingling  through  the  body's 
fibres. 

Such  being  the  relation  between  them,  the  difference  in  the  nature  of 
the  ideas  bodied  forth  in  music  and  in  architecture  becomes  readily  apparent. 
Music  is  interior,  abstract,  subjective,  speaking  directly  to  the  soul  in  a 
simple  and  universal  language  whose  meaning  is  made  personal  and  particu- 
lar in  the  breast  of  each  Hstener :  "Music  alone  of  all  arts,"  says  Balzac,  "has 
power  to  make  us  live  within  ourselves."  A  work  of  architecture  is  the  exact 
opposite  of  this ;  existing  principally  and  primarily  for  the  uses  of  the  body, 
it  is,  like  the  body,  a  concrete  organism,  attaining  to  esthetic  expression  only 
in  the  reconciliation  and  fulfilment  of  many  conflicting  practical  require- 
ments. Music  is  pure  beauty,  the  voice  of  the  unfettered  and  perpetually 
evanishing  soul  of  things;  architecture  is  that  soul  imprisoned  in  a  form, 
become  subject  to  the  law  of  casualty,  beaten  upon  by  the  elements,  at  war 
with  gravity,  the  slave  of  man.  One  is  the  Ariel  of  the  arts,  the  other,  Caliban. 

Coming  now  to  the  consideration  of  architecture  in  its  historical  rather 
than  in  its  philosophical  aspect,  it  will  be  shown  how  certain  theosophical 
concepts  are  applicable  here.  Of  these  none  is  more  familiar  and  none  more 
fundamental  than  the  idea  of  reincarnation.  By  reincarnation  more  than 
mere  physical  re-birth  is  implied,  for  physical  re-birth  is  but  a  single  mani- 
festation of  that  universal  law  of  alternation  of  state,  of  animation  of  vehicles, 
and  progression  through  successive  planes,  in  accordance  with  which  all 
things  move,  and  as  it  were  make  music, — each  cycle  complete,  yet  part  of  a 
larger  cycle,  the  incarnate  monad  passing  through  correlated  changes,  carry- 
ing along  and  bringing  into  manifestation  in  each  higher  arc  of  the  spiral  the 
experience  accumulated  in  all  preceding  states,  and  at  the  same  time  unfold- 
ing that  power  of  the  Self  peculiar  to  the  plane  in  which  it  happens  to  be 
manifesting. 

This  law  finds  exemplification  in  the  history  of  architecture  in  the  orderly 
flow  of  the  building  impulse  from  one  nation  and  one  country  to  a  diflferent 
nation  and  a  different  country:  its  new  vehicle  of  manifestation;  also  in  the 
continuity  and  increasing  complexity  of  the  development  of  that  impulse  in 
manifestation;  each  "incarnation"  summarizing  all  those  which  have  gone 
before,  and  adding  some  new  factor  peculiar  to  itself  alone;  each  being  a 


I  THE  ART  OF  ARCHITECTURE  13 

growth,  a  life,  with  periods  corresponding  to  childhood,  youth,  maturity  and 
decadence;  each  also  typifying  in  its  entirety  some  single  one  of  these  life 
periods,  and  revealing  some  special  aspect  or  power  of  the  Self. 

For  the  sake  of  clearness  and  brevity  the  consideration  of  only  one  of 
several  architectural  evolutions  will  be  attempted :  that  which,  arising  in  the 
north  of  Africa,  spread  to  southern  Europe,  thence  to  the  northwest  of 
Europe  and  to  England;  the  architecture,  in  short,  of  what  is  popularly 
known  as  the  civilized  world. 

This  architecture,  anterior  to  the  Christian  era,  may  be  broadly  divided 
into  three  great  periods,  during  which  it  was  successively  practiced  by  three 
peoples :  the  Egyptians,  the  Greeks,  and  the  Romans.  Then  intervened  the 
Dark  Ages,  and  a  new  art  arose,  the  Gothic,  which  was  a  flowering  out  in 
stone  of  the  spirit  of  Christianity.  This  was  in  turn  succeeded  by  the 
Renaissance,  the  impulse  of  which  remains  to-day  unexhausted.  In  each 
of  these  architectures  the  peculiar  genius  of  a  people  and  of  a  period  attained 
to  a  beautiful,  complete,  and  coherent  utterance,  and  notwithstanding  the 
considerable  intervals  of  time  which  sometimes  separated  them,  they  suc- 
ceeded one  another  logically  and  inevitably,  and  each  was  related  to  the  one 
which  preceded  and  which  followed  it  in  a  particular  and  intimate  manner. 

The  power  and  wisdom  of  ancient  Egypt  was  vested  in  its  priesthood, 
which  was  composed  of  individuals  exceptionally  qualified  by  birth  and 
training  for  their  high  office,  tried  by  the  severest  ordeals  and  bound  by 
the  most  solemn  oaths.  The  priests  were  honored  and  privileged  above  all 
other  men,  and  spent  their  lives  dwelling  apart  from  the  multitude  in  vast 
and  magnificent  temples,  dedicating  themselves  to  the  study  and  practice  of 
religion,  philosophy,  science,  and  art, — subjects  then  intimately  related,  not 
widely  separated  as  they  are  now.  These  men  were  the  architects  of  ancient 
Egypt;  theirs,  the  minds  which  directed  the  hands  that  built  those  time- 
defying  monuments. 

The  rites  which  the  priests  practiced  centered  about  what  are  known  as 
the  Lesser  and  the  Greater  Mysteries.  These  consisted  of  representations, 
by  means  of  symbol  and  allegory,  under  conditions  and  amid  surroundings 
the  most  awe-inspiring,  of  those  great  truths  concerning  man's  nature,  origin, 
and  destiny,  of  which  the  priests — in  reality  a  brotherhood  of  initiates  and 
their  pupils — were  the  custodians.  These  ceremonies  were  made  the  occasion 
for  the  initiation  of  neophytes  into  the  order,  and  the  advancement  of  the 
already  initiated  into  its  successive  degrees.    For  the  practice  of  such  rites, 


14  THE  BEAUTIFUL  NECESSITY  i 

and  others,  designed  to  impress  not  the  elect,  but  the  multitude,  the  great 
temples  of  Egypt  were  constructed.  Everything  about  them  was  calculated 
to  induce  a  deep  seriousness  of  mind,  and  to  inspire  feelings  of  awe,  dread, 
and  even  terror,  so  as  to  test  the  candidate's  fortitude  of  soul  to  the  utmost. 

The  avenue  of  approach  to  an  Egyptian  temple  was  flanked  on  either 
side,  sometimes  for  a  mile  or  more,  with  great  stone  sphinxes,  that  emblem 
of  man's  dual  nature,  the  god  emerging  from  the  beast.  The  entrance  was 
through  a  single  high  doorway  between  two  towering  pylons,  presenting  a 
vast  surface  sculptured  and  painted  over  with  many  strange  and  enigmatic 
figures  and  flanked  by  aspiring  obehsks,  and  seated  colossi  with  f  ace&  austere 
and  calm.  The  large  court  thus  entered  was  surrounded  by  high  walls  and 
colonnades,  but  was  open  to  the  sky.  Opposite  the  first  doorway  was 
another,  admitting  to  a  somewhat  smaller  enclosure,  a  forest  of  enormous 
carved  and  painted  columns  supporting  a  roof  through  the  apertures  of  which 
sunshine  gleamed,  or  dim  light  filtered  down.  Beyond  this,  in  turn,  were 
other  courts  and  apartments  culminating  in  some  inmost  sacred  sanctuary. 

Not  alone  in  their  temples,  but  in  their  tombs  and  pyramids,  and  all  the 
sculptured  monuments  of  the  Egyptians,  there  is  the  same  insistence  upon 
the  sublimity,  mystery,  and  awfulness  of  life,  which  they  seem  to  have  felt 
so  profoundly.  But  more  than  this,  the  conscious  thought  of  the  masters 
who  conceived  them,  the  buildings  of  Egypt  give  utterance  also  to  the  agony 
and  toil  of  the  thousands  of  slaves  and  captives  which  hewed  the  stones  out 
of  the  heart  of  the  rock,  dragged  them  long  distances,  and  placed  them  one 
upon  another,  so  that  these  buildings  oppress  while  they  inspire,  for  there  is 
in  them  no  freedom,  no  spontaneity,  no  individuality,  but  everywhere  the 
felt  presence  of  an  iron  conventionality,  of  a  stern,  immutable  law. 

In  Egyptian  architecture  is  symbolized  the  condition  of  the  human  soul 
awakened  from  its  long  sleep  in  nature,  and  become  conscious  at  once  of  its 
divine  source  and  of  the  leaden  burden  of  its  fleshly  envelope.  Egypt  is 
humanity  new  born,  bound  still  with  an  umbilical  cord  to  nature,  and  strong 
not  so  much  with  its  own  strength  as  with  the  strength  of  its  mother.  This 
idea  is  aptly  typified  in  those  gigantic  colossi  flanking  the  entrance  to  some 
rock-cut  temple,  which  though  entire  are  yet  part  of  the  living  clifT  out  of 
which  they  were  fashioned. 

In  the  architecture  of  Greece  the  note  of  dread  and  mystery  yields  to 
one  of  pure  joyousness  and  freedom.  The  terrors  of  childhood  have  been 
outgrown,  and  man  revels  in  the  indulgence  of  his  un jaded  appetites  and  in 


I  THE  ART  OF  ARCHITECTURE  15 

the  exercise  of  his  awakened  reasoning  faculties.  In  Greek  art  is  preserved 
that  evanescent  beauty  of  youth  which,  coming  but  once  and  continuing  but 
for  a  short  interval  in  every  human  life,  is  yet  that  for  which  all  antecedent 
states  seem  a  preparation,  and  of  which  all  subsequent  ones  are  in  some  sort 
an  effect.  Greece  typifies  adolescence,  the  love  age,  and  so  throughout  the 
centuries  humanity  has  turned  to  the  contemplation  of  her  just  as  a  man  all 
his  Hfe  long  secretly  cherishes  the  memory  of  his  first  love. 

An  impassioned  sense  of  beauty  and  an  enlightened  reason  characterize 
the  productions  of  Greek  architecture  during  its  best  period.  The  perfec- 
tion then  attained  was  possible  only  in  a  nation  whereof  the  citizens  were 
themselves  critics  and  amateurs  of  art,  one  wherein  the  artist  was  honored 
and  his  work  appreciated  in  all  its  beauty  and  subtlety.  The  Greek  architect 
was  less  bound  by  tradition  and  precedent  than  was  the  Egyptian,  and  he 
worked  unhampered  by  any  restrictions,  save  such  as,  like  the  laws  of  har- 
mony in  music,  helped  rather  than  hindered  his  genius  to  express  itself, — 
restrictions  founded  on  sound  reason,  the  value  of  which  had  been  proved 
by  experience. 

The  Doric  order  was  employed  for  all  large  temples,  since  it  possessed 
in  fullest  measure  the  qualities  of  simplicity  and  dignity,  the  attributes  appro- 
priate to  greatness.  Quite  properly,  also,  its  formulas  were  more  fixed  than 
those  of  any  other  style.  The  Ionic  order,  the  feminine  of  which  the  Doric 
may  be  considered  the  corresponding  masculine,  was  employed  for  smaller 
temples ;  like  a  woman,  it  was  more  supple  and  adaptable  than  the  Doric,  its 
proportions  were  more  slender  and  graceful,  its  lines  more  flowing,  and  its 
ornament  more  delicate  and  profuse.  A  freer  and  more  elaborate  style  than 
either  of  these,  infinitely  various,  seeming  to  obey  no  law  save  that  of  beauty, 
was  used  sometimes  for  small  monuments  and  temples,  such  as  the  Tower 
of  the  Winds,  and  the  monument  of  Lysicrates  at  Athens. 

Because  the  Greek  architect  was  at  liberty  to  improve  upon  the  work 
of  his  predecessors  if  he  could,  no  temple  was  just  like  any  other,  and  they 
form  an  ascending  scale  of  excellence,  culminating  in  the  Acropolis  group. 
Every  detail  was  considered  not  only  with  relation  to  its  position  and  func- 
tion, but  in  regard  to  its  intrinsic  beauty  as  well,  so  that  the  merest  fragment, 
detached  from  the  building  of  which  it  formed  a  part,  is  found  worthy  of 
being  treasured  in  our  museums  for  its  own  sake. 

Just  as  every  detail  of  a  Greek  temple  was  adjusted  to  its  position  and 
expressed  its  office,  so  the  building  itself  was  made  to  fit  its  site  and  to  show 


i6 


THE  BEAUTIFUL  NECESSITY 


forth  its  purpose,  forming  with  the  surrounding  buildings  a  unit  of  a  larger 
whole.  The  Athenian  Acropolis  is  an  illustration  of  this:  it  is  an  irregular 
fortified  hill,  bearing  diverse  monuments  in  various  styles,  at  unequal  levels 
and  at  different  angles  with  one  another,  yet  the  whole  arrangement  seems 
as  organic  and  inevitable  as  the  disposition  of  the  features  of  a  face.  The 
Acropolis  is  an  example  of  the  ideal  Architectural  Republic  wherein  each 
individual  contributes  to  the  welfare  of  all,  and  at  the  same  time  enjoys  the 
utmost  personal  liberty  (Illustration  i). 

Very  different  is  the  spirit  bodied  forth  in  the  architecture  of  Imperial 
Rome,  The  iron  hand  of  its  sovereignty,  encased  within  the  silken  glove 
of  its  luxury,  finds  its  prototype  in  buildings  which  were  stupendous  crude 
brute  masses  of  brick  and  concrete,  hidden  within  a  covering  of  rich  marbles 
and  mosaics,  wrought  in  beautiful,  but  often  meaningless  forms  by  clever, 
degenerate  Greeks.  The  genius  of  Rome  finds  its  most  characteristic  expres- 
sion, not  in  temples  to  the  high  gods,  but  rather  in  those  vast  and  complicated 


I  THE  ART  OF  ARCHITECTURE  17 

structures — basilicas,  amphitheatres,  baths — built  for  the  amusement  and 
purely  temporal  needs  of  the  people. 

If  Egypt  typifies  the  childhood  of  the  race  and  Greece  its  beautiful 
youth.  Republican  Rome  represents  its  strong  manhood, — a  soldier  filled 
with  the  lust  of  war  and  the  love  of  glory, — and  Imperial  Rome  its  degen- 
eracy: that  soldier  become  conqueror,  decked  out  in  plundered  finery  and 
sunk  in  sensuality,  tolerant  of  all  who  minister  to  his  pleasures  but  terrible 
to  all  who  interfere  with  them. 

The  fall  of  Rome  marked  the  end  of  the  ancient  Pagan  world.  Above  its 
ruin  Christian  civilization  in  the  course  of  time  arose.  Gothic  architecture 
is  an  expression  of  the  Christian  spirit;  in  it  is  manifest  the  reaction  from 
licentiousness  to  asceticism.  Man's  spiritual  nature,  awakening  in  a  body 
worn  and  weakened  by  debaucheries,  longs  ardently  and  tries  vainly  to 
escape.  Of  some  such  mood  a  Gothic  cathedral  is  the  expression ;  its  vault- 
ing, marvelously  supported  upon  slender  shafts  by  reason  of  a  nicely  adjusted 
equilibrium  of  forces ;  its  restless,  upward-reaching  pinnacles  and  spires ;  its 
ornament,  intricate  and  enigmatic ;  all  these  suggest  the  over-strained  organ- 
ism of  an  ascetic ;  while  its  vast,  shadowy  interior,  lit  by  marvelously  traceried 
and  jeweled  windows  which  hold  the  eyes  in  a  hypnotic  thrall,  is  like  his 
soul :  filled  with  world  sadness,  dead  to  the  bright,  brief  joys  of  sense,  seeing 
only  heavenly  visions,  knowing  none  but  mystic  raptures. 

Thus  it  is  that  the  history  of  architecture  illustrates  and  enforces  the 
theosophical  teaching  that  everything  of  man's  creating  is  made  in  his  own 
image.  Architecture  mirrors  the  life  of  the  individual  and  of  the  race, 
which  is  the  life  of  the  individual  written  large  in  time  and  space.  The 
terrors  of  childhood ;  the  keen  interests  and  appetites  of  youth ;  the  strong, 
stern  joy  of  conflict  which  comes  with  manhood;  the  lust,  the  greed,  the 
cruelty  of  a  materialized  old  age, — all  these  serve  but  as  a  preparation  for 
the  life  of  the  spirit,  in  which  the  man  becomes  again  as  a  little  child,  going 
over  the  whole  round,  but  on  a  higher  arc  of  the  spiral. 

The  final,  or  fourth  state  being  only  in  some  sort  a  repetition  of  the 
first,  it  would  be  reasonable  to  look  for  a  certain  correspondence  between 
Egyptian  and  Gothic  architecture,  and  such  a  correspondence  there  is,  though 
it  is  more  easily  divined  than  demonstrated.  In  both  there  is  the  same  deeply 
religious  spirit;  both  convey,  in  some  obscure  yet  potent  manner,  a  sense  of 
the  soul  being  near  the  surface  of  life.  There  is  the  same  love  of  mystery 
and  of  symbolism;  and  in  both  may  be  observed  the  tendency  to  create 


i8  THE  BEAUTIFUL  NECESSITY  i 

strange,  composite  figures  to  typify  transcendental  ideas,  the  sphinx  seem- 
ing a  blood  brother  to  the  gargoyle.  The  conditions  under  which  each  archi- 
tecture flourished  were  not  dissimilar,  for  each  was  formulated  and  con- 
trolled by  small,  well  organized  bodies  of  sincerely  religious  and  highly 
enlightened  men — the  priesthood  in  the  one  case,  the  masonic  guilds  in  the 
other — working  together  towards  the  consummation  of  great  undertakings 
amid  a  populace  for  the  most  part  oblivious  of  the  profound  and  subtle 
meanings  of  which  their  work  was  full.  In  Mediaeval  Europe,  as  in 
ancient  Egypt,  fragments  of  the  Secret  Doctrine — transmitted  in  the  symbols 
and  secrets  of  the  cathedral  builders — determined  much  of  Gothic 
architecture. 

The  architecture  of  the  Renaissance  period,  which  succeeded  the  Gothic, 
corresponds  again,  in  the  spirit,  which  animates  it,  to  Greek  architecture, 
which  succeeded  the  Egyptian;  for  the  Renaissance,  as  the  name  implies, 
was  nothing  other  than  an  attempt  to  revive  Classical  antiquity.  Scholars 
writing  in  what  they  conceived  to  be  a  Classical  style,  sculptors  modeling 
Pagan  deities,  and  architects  building  according  to  their  understanding  of 
Vitruvian  methods,  succeeded  in  producing  works  like,  yet  different  from 
the  originals  they  followed, — different  because,  animated  by  a  spirit  unknown 
to  the  ancients,  they  embodied  a  new  ideal. 

In  all  the  productions  of  the  early  Renaissance,  "that  first  transcendent 
springtide  of  the  modern  world,"  there  is  that  evanescent  grace  and  beauty 
of  youth  which  was  seen  to  have  pervaded  Greek  art,  but  it  is  a  grace  and 
beauty  of  a  different  sort.  The  Greek  artist  sought  to  attain  to  a  certain 
abstract  perfection  of  type;  to  build  a  temple  which  should  combine  all  the 
excellencies  of  every  similar  temple,  to  carve  a  figure  impersonal  in  the 
highest  sense,  which  should  embody  every  beauty.  The  artist  of  the  Renais- 
sance, on  the  other  hand,  delighted  not  so  much  in  the  type  as  in  the  variation 
from  it.  Preoccupied  with  the  unique  mystery  of  the  individual  soul — a 
sense  of  which  was  Christianity's  gift  to  Christendom — he  endeavored  to 
portray  that  wherein  a  particular  person  is  unique  and  singular.  Acutely 
conscious  also  of  his  own  individuality,  instead  of  effacing  it,  he  made  his 
work  the  vehicle  and  expression  of  that  individuality.  The  history  of 
Renaissance  architecture,  as  Symonds  has  pointed  out,  is  the  history  of  a 
few  eminent  individuals,  each  one  moulding  and  modifying  the  style  in  a 
manner  peculiar  to  himself  alone.  In  the  hands  of  Brunelleschi  it  was  stern 
and  powerful ;  Bramante  made  it  chaste,  elegant  and  graceful ;  Palladio  made 


THE  ART  OF  ARCHITECTURE 


19 


it  formal,  cold,  symmetrical;  while  with  Sansovino  and  Sammichele  it 
became  sumptuous  and  bombastic. 

As  the  Renaissance  ripened  to  its  decay,  architecture  assumed  more 
and  more  the  characteristics  which  distinguished  that  of  Rome  during  the 
decadence.  In  both  there  is  the  same  lack  of  simplicity  and  sincerity,  the 
same  profusion  of  debased  and  meaningless  ornament,  and  there  is  an 
increasing  disposition  to  conceal  and  falsify  the  construction  by  surface 
decoration. 

The  final  part  of  this  second,  or  modern  architectural  cycle  lies  still 
in  the  future.  It  is  not  unreasonable  to  believe  that  the  movement  towards 
mysticism,  of  which  modern  theosophy  is  a  phase  and  the  spiritualization  of 
science  an  episode,  will  flower  out  into  an  architecture  which  will  be  in  some 
sort  a  reincarnation  of  and  a  return  to  the  Gothic  spirit,  employing  new 
materials,  new  methods,  and  developing  new  forms  to  show  forth  ancient 
verities. 

In  studying  these  salient  periods  in  the  history  of  European  architecture, 
it  is  possible  to  trace  a  gradual  growth  or  unfolding,  as  of  a  plant.  It  is  a 
fact  fairly  well  established  that  the  Greeks  derived  their  architecture  and 
ornament  from  Egypt,  The  Romans  in  turn  borrowed  from  the  Greeks, 
while  a  Gothic  cathedral  is  a  lineal  descendant  from  a  Roman  basilica. 


._J^' 


The  Egyptians,  in  their  constructions,  did  little  more  than  to  place 
enormous  stones  on  end,  and  pile  one  huge  block  upon  another.  They  used 
many  columns  placed  close  together.  The  spaces  which  they  spanned  were 
inconsiderable.     The  upright,  or  supporting  member  may  be  said  to  have 


20 


THE  BEAUTIFUL  NECESSITY 


been  in  Egyptian  architecture  the  predominant  one.  A  vertical  Hne,  there- 
fore, may  be  taken  as  the  simplest  and  most  abstract  symbol  of  Egyptian 
architecture  (Illustration  2).  It  remained  for  the  Greeks  fully  to  develop 
the  lintel.  In  their  architecture  the  vertical  member,  or  column,  existed  solely 
for  the  sake  of  the  horizontal  member,  or  lintel ;  it  rarely  stood  alone,  as  in 
the  case  of  an  Egyptian  obelisk.    The  columns  of  the  Greek  temples  were 


mm 


■^  J  I  i  ftl  1 


^Ti  ,f\ 


n 


vr 


reduced  to  those  proportions  most  consistent  with  strength  and  beauty,  and 
the  intercolumnations  were  relatively  greater  than  in  Egyptian  examples. 
It  may  truly  be  said  that  Greek  architecture  exhibits  the  perfect  equality  and 
equipoise  of  vertical  and  horizontal  elements  and  these  only,  no  other  factor 
entering  in.  Its  graphic  symbol  would  therefore  be  composed  of  a  vertical 
and  a  horizontal  line  (Illustration  3).  The  Romans,  while  retaining  the 
column  and  lintel  of  the  Greeks,  deprived  them  of  their  structural  significance 
and  subordinated  them  to  the  semi-circular  arch,  and  the  semi-cylindrical  and 
hemispherical  vault,  the  truly  characteristic  and  determining  forms  of  Roman 
architecture.  Our  symbol  grows,  therefore,  by  the  addition  of  the  arc  of  a 
circle  (Illustration  4).  In  Gothic  architecture,  column,  lintel,  arch  and  vault 
are  all  retained  in  changed  form,  but  that  which  more  than  anything  else 
differentiates  Gothic  architecture  from  any  style  which  preceded  it,  is  the 
introduction  of  the  principle  of  an  equilibrium  of  forces,  of  a  state  of  balance 
rather  than  a  state  of  rest,  arrived  at  by  the  opposition  of  one  thrust  with 
another  contrary  to  it.  This  fact  can  be  indicated  graphically  by  two  opposing 


I  THE  ART  OF  ARCHITECTURE  21 

inclined  lines,  and  these  united  to  the  preceding  symbol  yield  an  accurate 
abstract  of  the  elements  of  Gothic  architecture  (Illustration  5). 

All  this  is  but  an  unusual  application  of  a  familiar  theosophic  teaching, 
namely,  that  it  is  the  method  of  nature  on  every  plane  and  in  every  depart- 
ment not  to  omit  anything  that  has  gone  before,  but  to  store  it  up  and  carry 
it  along  and  bring  it  into  manifestation  later.  Nature  everywhere  proceeds 
like  the  jingle  of  The  House  that  Jack  Built:  she  repeats  each  time  all  she 
has  learned,  and  adds  another  line  for  subsequent  repetition. 


II 

UNITY  AND   POLARITY 

THEOSOPHY,  both  as  a  doctrine,  or  system  of  thought  which  dis- 
covers correlations  between  things  apparently  unrelated,  and  as  a  life, 
or  system  of  training  whereby  it  is  possible  to  gain  the  power  to  per- 
ceive and  use  these  correlations  for  worthy  ends,  is  of  great  value  to  the 
creative  artist,  whose  success  depends  on  the  extent  to  which  he  works 
organically,  conforming  to  the  cosmic  pattern,  proceeding  rationally  and 
rhythmically  to  some  predetermined  end.  It  is  of  value,  no  less,  to  the  lay- 
man, the  critic,  the  art  amateur — to  anyone,  in  fact,  who  would  come  to  an 
accurate  and  intimate  understanding  and  appreciation  of  every  variety  of 
aesthetic  endeavor.  For  the  benefit  of  such  I  shall  try  to  trace  some  of  those 
correlations  which  theosophy  affirms,  and  indicate  their  bearing  upon  art, 
and  upon  the  art  of  architecture  in  particular. 

One  of  the  things  which  theosophy  teaches  is  that  those  transcendent 
glimpses  of  a  divine  order  and  harmony  throughout  the  universe  vouchsafed 
the  poet  and  the  mystic  in  their  moments  oi  vision  are  not  the  paradoxes — 
the  paronomasia,  as  it  were — of  an  intoxicated  state  of  consciousness,  but 
glimpses  of  reality.  We  are  all  of  us  participators  in  a  world  of  concrete 
music,  geometry  and  number, — a  world,  that  is,  of  sounds,  odors,  forms, 
motions,  colors,  so  mathematically  related  and  co-ordinated  that  our  pigmy 
bodies,  equally  with  the  farthest  star,  vibrate  to  the  music  of  the  spheres. 
There  is  a  Beautiful  Necessity  which  rules  the  world,  which  is  a  law  of  nature 
and  equally  a  law  of  art,  for  art  is  idealized  creation:  nature  carried  to 
a  higher  power  by  reason  of  its  passage  through  a  human  consciousness. 
Thought  and  emotion  tend  to  crystallize  into  forms  of  beauty  as  inevitably 

[22] 


II  UNITY  AND  POLARITY  23 

as  does  the  frost  on  a  window  pane.  Art,  therefore,  in  one  of  its  aspects,  is 
the  weaving  of  a  pattern,  the  communication  of  an  order  and  a  method  to  the 
material  or  medium  employed.  Although  no  masterpiece  was  ever  created 
by  the  conscious  following  of  set  rules,  for  the  true  artist  works  uncon- 
sciously, instinctively,  as  the  bird  sings,  or  as  the  bee  builds  its  honey-cell, 
yet  an  analysis  of  any  masterpiece  reveals  the  fact  that  its  author  (like  the 
bird  and  the  bee)  has  "followed  the  rules  without  knowing  them." 

Helmholtz  says,  "No  doubt  is  now  entertained  that  beauty  is  subject 
to  laws  and  rules  dependent  on  the  nature  of  human  intelligence.  The 
difficulty  consists  in  the  fact  that  these  laws  and  rules,  on  whose  fulfilment 
beauty  depends,  are  not  consciously  present  in  the  mind  of  the  artist  who 
creates  the  work,  or  of  the  observer  who  contemplates  it."  Nevertheless 
they  are  discoverable,  and  can  be  formulated,  after  a  fashion.  We  have  only 
to  read  aright  the  lesson  of  the  Good  Law  everywhere  portrayed  in  the  vast 
picture-book  of  nature  and  of  art. 

The  first  truth  therein  published  is  the  law  of  Unity — oneness ;  for  there 
is  one  Self,  one  Life,  which,  myriad  in  manifestation,  is  yet  in  essence  ever 
one.  Atom  and  universe,  man  and  the  world,  each  is  a  unit,  an  organic  and 
coherent  whole.  The  application  of  this  law  to  art  is  so  obvious  as  to  be 
almost  unnecessary  of  elucidation,  for  to  say  that  a  work  of  art  must  possess 
unity,  miist  seem  to  proceed  from  a  single  impulse  and  be  the  embodiment 
of  one  dominant  idea,  is  to  state  a  truism.  In  a  work  of  architecture  the  co- 
ordination of  its  various  parts  with  one  another  is  almost  the  measure  of  its 
success.  We  remember  any  masterpiece — the  cathedral  of  Paris  no  less 
than  the  pyramids  of  Egypt — by  the  singleness  of  its  appeal;  complex  it 
may  be,  but  it  is  a  co-ordinated  complexity ;  variety  it  may  possess,  but  it  is 
a  variety  in  an  all-embracing  unity. 

The  second  law,  not  contradicting,  but  supplementing  the  first,  is  the 
law  of  Polarity,  i.  e,,  duality.  All  things  have  sex,  are  either  masculine  or 
feminine.  This,  too,  is  the  reflection,  on  a  lower  plane,  of  one  of  those 
transcendental  truths  taught  by  the  Ancient  Wisdom,  namely  that  the  Logos, 
in  His  voluntarily  circumscribing  His  infinite  life  in  order  that  He  might 
manifest,  incloses  himself  within  his  limiting  veil,  Maya,  and  that  His  Life 
appears  as  Spirit  (male)  and  his  Maya  as  Matter  (female),  the  two  being 
never  disjointed  during  manifestation.  The  two  terms  of  this  polarity  are 
endlessly  repeated  throughout  nature:  in  sun  and  moon,  day  and  night,  fire 
and  water,  man  and  woman — and  so  on.     A  close  inter-relation  is  always 


24  THE  BEAUTIFUL  NECESSITY  ii 

discerned  to  subsist  between  corresponding  members  of  such  pairs  of  oppo- 
sites :  sun,  day,  fire,  man,  express  and  embody  the  primal  and  active  aspect  of 
the  manifesting  deity;  moon,  night,  water,  woman,  its  secondary  and  pas- 
sive. Moreover,  each  in  a  sense  impHes,  or  brings  to  mind,  the  others  of  its 
class:  man,  like  the  sun  is  lord  of  day,  a  direct  and  devastating  force  like 
fire;  woman  is  subject  to  the  lunar  rhythm;  like  water,  she  is  soft,  sinuous, 
fecund. 

The  part  which  this  polarity  plays  in  the  arts  is  important,  and  the 
constant  and  characteristic  distinction  between  the  two  terms  is  a  thing  far 
beyond  mere  contrast. 

In  music  they  are  the  major  and  the  minor  modes :  the  typical,  or 
representative  chords  of  the  dominant  seventh  and  of  the  tonic  (the  two 
chords  into  which  Schopenhauer  affirms  all  music  can  be  resolved),  a  partial 
dissonance  and  a  consonance^a  chord  of  suspense  and  a  chord  of  satisfacjion. 
In  speech  the  two  are  vowel  and  consonant  sounds,  the  type  of  the  first  being 
a,  a  sound  of  suspense,  made  with  the  mouth  open,  and  of  the  second  m,  a 
sound  of  satisfaction,  made  by  closing  the  mouth;  their  combination  forms 
the  sacred  syllable  Om.  In  painting  they  are  warm  colors  and  cold,  the  pole 
of  the  first  being  in  red,  the  color  of  fire,  which  excites,  and  of  the  second 
in  blue,  the  color  of  water,  which  calms ;  in  the  arts  of  design  they  are  lines 
straight  (like  fire),  and  flowing  (like  water)  ;  masses  light  (like  the  day), 
and  dark  (like  flight).  In  architecture  they  are  the  column,  or  supporting 
member,  which  resists  the  force  of  gravity,  and  the  horizontal  member,  or 
lintel,  which  succumbs  to  it ;  they  are  vertical  lines,  which  are  aspiring,  effort- 
ful, and  horizontal  lines,  which  are  restful  to  the  eye  and  mind. 

It  is  desirable  to  have  an  instant  and  keen  realization  of  this  sex  quality, 
and  to  make  this  easier,  some  sort  of  a  classification  and  analysis  must  be 
attempted.  Those  things  which  are  allied  to,  and  partake  of  the  nature  of 
time  are  masculine,  and  those  which  are  allied  to  and  partake  of  the  nature 
of  space  are  feminine,  as  motion  and  matter,  mind  and  body,  etc.  The 
English  words  "masculine"  and  "feminine"  are  too  intimately  associated 
with  the  idea  of  physical  sex  properly  to  designate  the  terms  of  this  polarity. 
In  Japanese  philosophy  and  art  the  two  are  called  In  and  Yo  (In,  feminine; 
Yo,  masculine),  and  these  little  words,  being  free  from  the  limitations  of 
their  English  correlatives,  will  be  found  convenient,  Yo  to  designate  that 
which  is  simple,  direct,  primary,  active,  positive ;  and  In,  that  which  is  com- 
plex, indirect,  derivative,  passive,  negative.     Things  hard,  straight,  fixed. 


II 


UNITY  AND  POLARITY 


25 


vertical  are  Yo ;  things 
soft,  curved,  horizontal, 
fluctuating  are  In,  and 
so   on. 

In  passing  it  may  be 
said  that  the  superiority  of 
the  line,  mass,  and  color 
composition  of  Japanese 
prints  and  kakemonos  to 
that  exhibited  in  the  vastly 
more  pretentious  easel  pictures  of  modern  Occidental  artists — a  superiority 
now  generally  acknowledged  by  connoisseurs — is  largely  due  to  the  con- 
scious following,  on  the  part  of  the  Japanese,  of  this  principle  of  sex- 
complementaries. 

Nowhere  are  In  and  Yo  more  simply  and  adequately  imaged  than  in 
the  vegetable  kingdom.  The  trunk  of  a  tree  is  Yo,  its  foliage,  In;  and  in 
each  stem  and  leaf  the  two  are  repeated.  A  calla,  consisting  of  a  single 
straight  and  rigid  spadix  embraced  by  a  soft  and  tenderly  curved  spathe, 
affords  an  almost  perfect  expression  of  the  characteristic  differences  between 
Yo  and  In  and  their  reciprocal  relation  to  each  other.  The  two  are  not  often 
combined  in  such  simplicity  and  perfection  in  a  single  form.  The  straight, 
vertical  reeds  which  so  often  grow  in  still,  shallow  water,  find  their  comple- 
ment in  the  curved  lily-pads  which  lie  horizontally  on  its  surface.  Trees 
such  as  the  pine  and  hemlock,  which  are  excurrent — those  in  which  the 
branches  start  successively  (i.  e.,  after  the  manner  of  time)  from  a  straight 
and  vertical  central  stem — are  Yo ;  trees  such  as  the  elm  and  willow,  which 
are  deliquescent, — those  in  which  the  trunk  dissolves,  as  it  were,  simultane- 
ously (after  the  manner  of  space)  into  its  branches,  are  In.  All  tree  forms 
lie  in  or  between  these  two  extremes,  and  leaves  are  susceptible  of  a  similar 
classification.  It  will  be  seen  to  be  a  classification  according  to  time  and 
space,  for  the  characteristic  of  time  is  succession,  and  of  space  simultaneous- 
ness;  the  first  is  expressed  symbolically  by  elements  arranged  with  relation 
to  axial  lines ;  the  second,  by  elements  arranged  with  relation  to  focal  points 
(Illustrations  6,  7). 

The  art  student  should  train  himself  to  recognize  In  and  Yo  in  all  their 
Protean  presentments  throughout  nature, — in  the  cloud  upon  the  mountain, 
the  wave  against  the  cliff,  in  the  tracery  of  trees  against  the  sky, — that  he 


26 


THE  BEAUTIFUL  NECESSITY 


II 


THE  LAW  OF  POLAR.ITY 


may  the  more  readily  recognize  them  in  his  chosen  art,  whatever  that  art 
may  be.  If  it  happens  to  be  painting,  he  will  endeavor  to  discern  this  law 
of  duality  in  the  composition  of  every  masterpiece,  recognizing  an  instinctive 
obedience  to  it  in  that  favorite  device  of  the  great  Renaissance  masters  of 
making  an  architectural  setting  for  their  groups  of  figures,  and  he  will  delight 
to  trace  the  law  in  all  its  ramifications  of  contrast  between  complementaries 
in  line,  color  and  mass  (Illustration  8). 

With  reference  to  architecture,  as  a  general  proposition  it  is  true  that 
architectural  forms  have  been  developed  through  necessity,  the  function 
seeking  and  finding  its  appropriate  form.  For  example,  the  buttress  of  a 
Gothic  cathedral  was  developed  by 
the  necessity  of  resisting  the  thrust 
of  the  interior  vaulting  without  en- 
croaching upon  the  nave;  the  main 
lines  of  a  buttress  conform  to  the 
direction  of  the  thrust,  and  the  pin- 
nacle with  which  it  terminates  is  a 
logical  shape  for  the  masonry  neces- 
sary to  hold  the  top  in  position  (Il- 
lustration 9).  Research  along  these 
lines  is  very  interesting  and  fruitful 
of  result,  but  there  remains  a  certain 
number  of  architectural  forms  whose 
origin  cannot  be  explained  in  any 
such  manner.  The  secret  of  their 
undying  charm  lies  in  the  fact  that 
in  them  In  and  Yo  stand  symbolized 
and  contrasted.  They  no  longer 
obey  a  law  of  utility,  but  an  abstract 
law  of  beauty,  for  in  becoming  sexu- 
ally expressive,  as  it  were,  the  con- 
struction itself  is  sometimes  weak- 
ened or  falsified.  The  familiar 
classic  console  or  modillion  is  an 
example:  although  in  general  con- 
tour it  is  well  adapted  to  its  function  as  a  supporting  bracket,  embedded  in, 
and  projecting  from  a  wall,  yet  the  scroll-like  ornament  with  which  its  sides 


^&m 


CLEOPATRA  MELTING  THE 
PEARL,  £>V  TIEPOLO' 


II 


UNITY  AND  POLARITY 


27 


are  embellished  gives  it  the  appearance  of  not  entering 
the  wall  at  all,  but  of  being  stuck  against  it  in  some 
miraculous  manner.  This  defect  in  functional  expressive- 
ness is  more  than  compensated  for  by  the  perfection 
with  which  feminine  and  masculine  characteristics  are 
expressed  and  contrasted  in  the  exquisite  double  spiral, 
opposed  to  the  straight  lines  of  the  moulding  which  it 
subtends  (Illustration  10).  Again,  by  fluting  the  shaft 
of  a  column  its  area  of  cross-section  is  diminished  but 
the  appearance  of  strength  is  enhanced,  because  its  mascu- 
line character — as  a  supporting  member  resisting  the  force 
of  gravity — is  emphasized. 

The  importance  of  the  so-called  "orders"  lies  in  the 
'  fact  that  they  are  architecture  epitomized,  as  it  were.    A 

building  consists  of  a  wall  upholding  a  roof :  support  and  weight ;  the  type 
of  the  first  is  the  column,  which  may  be  conceived  of  as  a  condensed  section 
of  wall,  and  of  the  second  the  lintel,  which  may  be  conceived  of  as  a  con- 
densed section  of  roof.  The  column,  being  vertical,  is  Yo;  the  lintel,  being 
horizontal,  is  In.  To  mark  an  entablature  with  horizontal  lines  in  the  form 
of  mouldings,  and  the  columns  with  vertical  lines  in  the  form  of  flutes,  as  is 
done  in  all  the  so-called  Classic  Orders,  is  a 
gain  in  functional  and  sex  expressiveness,  and 
consequently  in  art  (Illustration  11). 

The  column  is  again  divided  into  the  shaft,, 
which  is  Yo,  and  the  capital,  which  is  In.  The 
capital  is  itself  twofold,  consisting  of  a  curved 
member  and  an  angular  member.  These  two 
appear  in  their  utmost  simplicity  in  the  echinus 
(In),  and  the  abacus  (Yo)  of  a  Greek  Doric 
cap.  The  former  was  adorned  with  painted 
leaf  forms,  characteristically  feminine,  and  the 
latter  with  the  angular  fret  and  meander  (Il- 
lustration 12).     The  Ionic  capital,  belonging 

to  a  more  feminine  style,  exhibits  the  abacus  subordinated  to  that  beautiful 
cushion-shaped  member  with  its  two  spirally  marked  volutes.  This,  though 
a  less  rational  and  expressive  form  for  its  particular  office  than  is  the  echinus 
of  the  Doric  cap,  is  a  far  more  perfect  symbol  of  the  feminine  element  in 


COKJLNTHIAN  MODILUON 


p=: — ~:::=r  classic 

{^J^y^O  CONSOLE 


28 


THE  BEAUTIFUL  NECESSITY 


II 


nature.  There  is  an  essential  identity  between 
the  Ionic  cap  and  the  Classic  console  before 
referred  to,  although  superficially  the  two  do  not 
resemble  one  another,  as  a  straight  line  and  a 
double  spiral  are  elements  common  to  both  (Il- 
lustration lo).  The  Corinthian  capital  consists 
of  an  ordered  mass  of  delicately  sculptured  leaf 
and  scroll  forms  sustaining  an  abacus  which, 
though  relatively  masculine,  is  yet  more  curved 
and  feminine  than  that  of  any  other  style.  In 
the  caulicole  of  a  Corinthian  cap  In  and  Yo  are 
again  contrasted.  In  the  unique  and  exquisite 
capital  from  the  Tower  of  the  Winds,  at  Athens, 
the  two  are  well  suggested  in  the  simple,  erect, 
and  pointed  leaf  forms  of  the  upper  part,  con- 
trasted with  the  complex,  deliquescent,  rounded  ones  from  which  they  spring. 
The  essential  identity  of  principle  subsisting  between  this  cap  and  the  Renais- 
sance baluster  by  San  Gallo  is  apparent  (Illustration  13). 

This  law  of  sex-expressiveness  is  of  such  universality  that  it  can  be 
made  the  basis  of  an  analysis  of  the  architectural  ornament  of  any  style  or 
period.  It  is  more  than  mere  opposition  and  contrast.  The  egg  and  tongue 
motif,  which  has  persisted  throughout  so  many  centuries  and  survived  so 
many  styles,  exhibits  an  alternation  of  forms  resembling  phallic  emblems. 
Yo  and  In  are  well  suggested  in  the  channel  triglyphs  and  the  sculptured 
metopes  of  a  Doric  frieze,  in  the  straight  and  vertical  mullions  and  the 
flowing  tracery  of  Gothic 
windows,  in  the  banded 
torus,  the  bead  and  reel, 
and  other  familiar  orna- 
mented mouldings  (Il- 
lustrations 14,  15,  16). 

There  are  indications 
that  at  some  time  dur- 
ing the  development  of 
Gothic  architecture  in 

France,  this  sex-distinction  became  a  recognized  principle,  moulding  and 
modifying  the  design  of  a  cathedral  in  much  the  same  way  that  sex  modifies 


-Yo  - — ^^SSEMME 


-* IN  ->> 


GRjBCIAN  DORIC  CAP 


lONIG  CAP 


II 


UNITY  AND  POLARITY 


29 


bodily  structure.  The  ma- 
sonic guilds  of  the  Middle 
Ages  were  custodians  of  the 
esoteric — which  is  the  the- 
osophic — side  of  the  Chris- 
tian faith,  and  every  student 
of  the  Secret  Doctrine  knows 
how  fundamental  and  far- 
reaching  is  this  idea  of  sex. 
The  entire  cathedral  sym- 
bolized the  crucified  body  of 
Christ;  its  two  towers,  man 
and  woman — that  Adam  and 
Eve,  for  whose  redemption, 
according  to  popular  belief, 
Christ  suffered  and  was  cru- 
cified. The  north,  or  right 
hand  tower  ("the  man's 
side")  was  called  the  sacred 
male  pillar,  Jachin;  and  the 


wmE\ 


CORINTHIAN  CAP 
nJiOM  HADR>IAN 
BU1LD1NG5. 

JCTKLm. 


rt-YO 


RO^BTTR  FItOM 
TEMPLE;  O^  MAE.$, 
EOMB 


CA.ULICULUJII 
OFOORJNTHIAN 
CAP 


BALUJTBIb  3Y  SAN  QALLO 


13 


YOINVD 

M 

U 

M 

0 

EOOANDTONQUL 
YD  IN 


south,  or  left  hand  tower  ("the  woman's  side") 
the  sacred  female  pillar,  Boaz,  from  the  two 
columns  flanking  the  gate  to  Solomon's  Temple 
— itself  an  allegory  of  the  bodily  temple.  In 
only  a  few  of  the  French  cathedrals  is  this 
distinction  clearly  and  consistently  maintained, 
and  of  these  Tours  forms  perhaps  the  most 
remarkable  example,  for  in  its  flamboyant 
facade,  over  and  above  the  difference  in  actual 
breadth  and  apparent  sturdiness  of  the  two 
towers  (the  south  being  the  more  slender  and 
delicate),  there  is  a  clearly  marked  distinction 
in  the  character  of  the  ornamentation,  that  of 
the  north  tower  being  more  salient,  angular, 
radial — more  masculine,  in  point  of  fact  ( Illus- 
tration 17).  In  Notre  Dame,  the  cathedral  of  Paris,  as  in  the  cathedral  of 
Tours,  the  north  tower  is  perceptibly  broader  than  the  south.     The  only 


5EADANDR£SL 


BANDED  TORUS 


14 


30 


THE  BEAUTIFUL  NECESSITY 


II 


VO       IN        YO      IN 


m  H  h  IM  H  h  ti  H  H  H  l-i 


FRIKZE  OF  TH)  EAJWSTESE.  PALACE/ 


'^'.-v'/.-.tJ^ 


ROMAN  CONSOLE. 
\ATICAN  MU5&UM 


FRIEZE  IN  THE  EMPIRE,  5TYLE 
BY  PBRCIER  AND  FONTAINE^. 

YD     IN      YO     IN 


FRIE2&  FROM  THE 
.     TEMPLE  OF  VESTA 
AT  TI VOLI .  (ROMAN) 


ROMAN  DOR^IG  FRJBZE VIGNOLE 


15 

other  important  difference  appears  to  be  in  the  angular  label  mould  above 
the  north  entrance :  whatever  may  have  been  its  original  function  or  signifi- 
cance, it  serves  to  define  the  tower  sexually,  so  to  speak,  as  effectively  as 
does  the  beard  on  a  man's  face.  In  Amiens  the  north  tower  is  taller  than 
the  south,  and  more  massive  in  its  upper  stages.  The  only  traceable  indica- 
tion of  sex  in  the  ornamentation  occurs  in  the  spandrels  at  the  sides  of  the 
entrance  arches :  those  of  the  north  tower  containing  single  circles,  and  those 
of  the  south  tower  containing  two.  This  difference,  small  as  it  may  seem,  is 
significant,  for  in  Europe  during  the  Middle  Ages,  just  as  anciently  in  Egypt, 
and  again  in  Greece — in  fact  wherever  and  whenever  the  Secret  Doctrine 
was  known — sex  was  attributed  to  numbers,  odd  numbers  being  conceived  of 


II 


UNITY  AND  POLARITY 


31 


YOIN 


EGYPTIAN  ORNAMENT 
YOIN 

GRiEEIC  ORNAMENT 
yo  IN 


PALAZZO  CIRAUD.  RQKfi 
VO    IN 


lALAZZO  FARJNESK  RONE 
VDIN 


QRHfiK.  HONEYSUOKLS 


as  masculine  and  even  as  feminine.  Two,  the 
first  feminine  number,  thus  became  a  symbol 
of  femininity,  accepted  as  such  so  universally 
at  the  time  the  cathedrals  were  built,  that  two 
strokes  of  a  bell  announced  the  death  of  a 
woman,  three  the  death  of  a  man. 

The  vital,  organic  quality  so  conspicuous 
in  the  best 
Gothic  archi- 
tecture has 
been  attributed 
to  the  fact  that 
necessity  deter- 
mined its  char- 
acteristic forms.  Professor  Goodyear  has 
demonstrated  that  it  may  be  due  also  in  part 
to  certain  subtle  vertical  leans  and  horizontal 
bends ;  and  to  nicely  calculated  variations  from 
strict  uniformity,  which  find  their  analogue  in 
nature,  where  structure  is  seldom  rigidly 
geometrical.  The  author  hazards  the  theory  that  still  another  reason  why  a 
Gothic  cathedral  seems  so  living  a  thing  is  because  it  abounds  in  contrasts 
between  what,  for  lack  of  more  descriptive  adjectives,  he  is  forced  to  call 
masculine  and  feminine  forms. 

Ruskin  says,  in  "Stones  of  Venice,"  "All  good  Gothic  is  nothing  more 
than  the  development,  in  various  ways,  and  on  every  conceivable  scale,  of 
the  group  formed  by  the  pointed  arch  for 
the  bearing  line  below,  and  the  gable  for 
the  protecting  line  above,  and  from  the 
huge,  gray,  shaly  slope  of  the  cathedral 
roof,  with  its  elastic  pointed  vaults  be- 
neath, to  the  crown-like  points  that  enrich 
the  smallest  niche  of  its   doorway,   one 
law  and  one  expression  will  be  found  in 
all.    The  modes  of  support  and  of  decora- 
tion are  infinitely  various,  but  the  real  character  of  the  building,  in  all  good 
Gothic,  depends  on  the  single  lines  of  the  gable  over  the  pointed  arch 


16 


GOTHIC/ 


r^ 


ClASSIO 


THE  ELEMENTS  CP  OOTHIC  CO 
AND  O^  CXASSICC2)  AEX2HITECTURE/ 


32 


THE  BEAUTIFUL  NECESSITY 


II 


endlessly  rearranged  and  repeated."     These 

two,  an  angular  and  a  curved  form,  like  the 

everywhere  recurring  column  and  lintel  of 

classic  architecture,  are  but  presentments  of 

Yo  and  In  (Illustration  i8).    Every  Gothic 

traceried  window,  with  straight  and  vertical 

mullions  in  the  rectangle,  losing  themselves 

in  the  intricate  foliations  of  the  arch,  cele- 
brates the  marriage  of  this  ever  diverse  pair. 

The  circle  and  the  triangle  are  the  In  and  Yo 

of  Gothic  tracery,  its  Eve  and  Adam,  as  it 

were,    for    from    their    union    springs    that 

progeny  of  trefoil,  quatrefoil,  cinquefoil,  of 

shapes  flowing  like  water,  and  shapes  darting 

like  flame,  which  make  such  visible  music  to  the  entranced  eye. 

By  seeking  to  discover  In  and  Yo  in  their  myriad  manifestations,  by 

learning  to  discriminate  between  them,  and  by  attempting  to  express  their 

characteristic  qualities  in  new  forms  of  beauty — from  the  disposition  of  a 

fagade  to  the  shaping  of  a  moulding — 
the  architectural  designer  will  charge 
his  work  with  that  esoteric  significance, 
that  excess  of  beauty,  by  which  archi- 
tecture rises  to  the  dignity  of  a  "fine" 
art  (Illustrations  19,  207.  In  so  doing, 
however,  he  should  never  forget,  and 
the  layman,  also,  should  ever  remember, 
that  the  supreme  architectural  excel- 
lence is  fitness,  appropriateness,  the 
perfect  adaptation  of  means  to  ends, 
and  the  perfect  expression  of  both 
means  and  ends.  These  two  aims,  the 
one  abstract  and  universal,  the  other 
concrete  and  individual,  can  always  be 
combined,  just  as  in  every  human 
countenance  are  combined  a  type,  which 
is  universal,  and  a  character,  which  is 
individual. 


SAN  QIMiaNANO  5.  JACOPO. 


20 


Ill 

CHANGELESS  CHANGE 

TRINITY,  CONSONANCE,  DIVERSITY  IN  MONOTONY, 
BALANCE,  RHYTHMIC  CHANGE,  RADIATION 

THE  preceding  essay  was  devoted  for  the  most  part  to  that  "inevitable 
duahty"  which  finds  concrete  expression  in  countless  pairs  of 
opposites,  such  as  day  and  night,  fire  and  water,  man  and  woman; 
in  the  art  of  music  by  two  chords,  one  of  suspense  and  the  other  of  fulfil- 
ment; in  speech  by  vowel  and  consonant  sounds,  epitomized  in  a  and  in  m; 
in  painting  by  warm  colors  and  cold,  epitomized  in  red  and  blue;  in  archi- 
tecture by  the  vertical  column  and  the  horizontal  lintel,  by  void  and  solid, — 
and  so  on. 

TRINITY 

This  concept  should  now  be  modified  by  another,  namely:  that  in  every 
duality  a  third  is  latent ;  that  two  implies  three,  for  each  sex,  so  to  speak,  is 
in  process  of  becoming  the  other,  and  this  alternation  engenders  and  is  accom- 
plished by  means  of  a  third  term,  or  neuter,  which  is  like  neither  of  the 
original  two,  but  partakes  of  the  nature  of  them  both,  just  as  a  child  may 
resemble  both  its  parents.  Twilight  comes  between  day  and  night ;  earth  is 
the  child  of  fire  and  water ;  in  music,  besides  the  chord  of  longing  and  striv- 
ing and  the  chord  of  rest  and  satisfaction  (the  dominant  seventh  and  the 
tonic)  there  is  a  third,  or  resolving  chord,  in  which  the  two  are  reconciled.  In 
the  sacred  syllable  Om,  which  epitomizes  all  speech,  the  u  sound  effects  the 
transition  between  the  a  sound  and  the  m;  among  primary  colors  yellow 
comes  between  red  and  blue;  and  in  architecture  the  arch,  which  is  both 

[33] 


34 


THE  BEAUTIFUL  NECESSITY 


III 


THE;  LAW  OF  TRINITY: 


A  ROMAN  lO^irCARGADt  &Y 
VIONOLLr-THE  CXDLUMN.  THE. 
ENTAElATURi.  AND  THL  ARCH 
CORRi^SPOND  TX)  LlNM  V&foT: 
ICAI.  HORIZONTAL  AND  CURVED 


weight  and  support,  which  is  neither  vertical 
nor  horizontal,  may  be  considered  the  neuter 
of  the  group  of  which  the  column  and  the 
lintel  are  respectively  masculine  and  feminine. 
"These  are  the  three,"  says  Mr,  Louis  Sulli- 
van, "the  only  three  letters  from  which  has 
been  expanded  the  architectural  art,  as  a 
great  and  superb  language  wherewith  man 
has  expressed,  through  the  generations,  the 
changing  drift  of  his  thoughts." 

It  would  be  supererogatory  to  dwell  at  any 
length  on  this  "trinity  of  manifestation"  as 
the  concrete  expression  of  that  unmanifest 
and  mystical  trinity,  that  three-in-one  which 
under  various  names  occurs  in  every  world- 
religion,  where,  defying  definition,  it  was 
wont  to  find  expression  symbolically,  in  some 
combination  of  vertical,  horizontal,  and 
curved  lines.  The  ansated  cross  of  the 
Egyptians  is  such  a  symbol,  the  Buddhist 
wheel,  and  the  flyflot,  or  swastika  inscribed  within  a  circle ;  also  those 
numerous  Christian  symbols  combining  the  circle  and  the  cross.  Such 
ideographs  have  spelled  profound  meaning  to  the  thinkers  of  past  ages.  We 
of  to-day  are  not  given  to  discovering  anything  wonderful  in  three  strokes 
of  a  pen,  but  every  artist,  in  the  weaving  of  his  pattern,  must  needs  employ 
these  mystic  symbols,  in  one  form  or  another,  and  if  he  employs  them  with 
a  full  sense  of  their  hidden  meaning,  his  work  will  be  apt  to  gain  in  originality 
and  beauty, — for  originality  is  a  new  and  personal  perception  of  beauty,  and 
beauty  is  the  name  we  give  to  truth  we  cannot  understand. 

In  architecture,  this  trinity  of  vertical,  horizontal  and  curved  lines  finds 
admirable  illustration  in  the  application  of  columns  and  entablature  to  an 
arch  and  impost  construction,  so  common  in  Roman  and  Renaissance  work. 
This  is  a  redundancy,  and  finds  no  justification  in  the  reason,  since  the  weight 
is  sustained  by  the  arch,  and  the  "order"  is  an  appendage  merely,  yet  the 
combination,  illogical  as  it  is,  satisfies  the  sense  of  beauty,  because  the  arch 
effects  a  transition  between  the  columns  and  the  entablature,  and  completes 
the  trinity  of  vertical,  horizontal,  and  curved  lines   (Illustration  21).     In 


21 


Ill 


CHANGELESS  CHANGE 


35 


THE  LAW  Of^  TWNITY 


the  entrances  to  many  of  the  Gothic  cathedrals  and  churches  the  same 
elements  are  better  because  more  logically  disposed.  Here  the  horizontal 
lintel  and  its  vertical  supports  are  not  decorative  merely,  but  really  perform 
their  proper  functions,  while  the  arch,  too,  has  a  raison  d'etre  in  that  it  serves 
to  reHeve  the  lintel  of  the  superincumbent  weight  of  masonry.  The  same  ar- 
rangement sometimes  occurs  in  Classic  architecture  also,  as  when  an  opening 
spanned  by  a  single  arch  is  subdivided  by  means  of  an  order  (Illustration  22). 

Three  is  pre-eminently  the 
number  of  architecture,  because 
it  is  the  number  of  our  space, 
which  is  three-dimensional,  and 
of  all  the  arts  architecture  is 
most  concerned  with  the  expres- 
sion of  spatial  relations.  The 
division  of  a  composition  into 
three  related  parts  is  so  universal 
that  it  would  seem  to  be  the  re- 
sult of  an  instinctive  action  of 
the  human  mind.  The  twin 
pylons  of  an  Egyptian  temple, 
with  its  entrance  between,  for  a 
third  division,  has  its  corre- 
spondence in  the  two  towers  of 
a  Gothic  cathedral  and  the  inter- 
vening screen  wall  of  the  nave. 
In  the  palaces  of  the  Renaissance 
a  three-fold  division — vertically 
by  means  of  quoins  or  pilasters,  ^ 

and  horizontally  by  means  of  cornices  or  string  courses — was  common,  as 
was  also  the  division  into  a  principal  and  two  subordinate  masses  (Illustra- 
tion 23). 

The  architectural  "orders,"  so-called,  are  divided  threefold  into  pedestal 
or  stylobate,  column,  and  entablature;  and  each  of  these  is  again  divided 
threefold ;  the  first  into  plinth,  die,  and  cornice ;  the  second  into  base,  shaft, 
and  capital;  the  third  into  architrave,  frieze,  and  cornice.  In  many  cases 
these  again  lend  themselves  to  a  threefold  subdivision.  A  more  detailed 
analysis  of  the  capitals  already  shown  to  be  twofold  reveals  a  third  member : 


THE  TPJNTTV  OF^  HORJZDNTAL- 
^•^VEItTICAL.AND  CURVED  UNE$ 


36 


THE  BEAUTIFUL  NECESSITY 


III 


THE/  hfiish/  OF  trinity:  A  THRLLFOLD  DIS- 
POSITION OF  TH£  PAET$  OF  A  BUILDING— 


■■tLlJil^iL.Llli 


GOTHIC-NOTRt  DAML. 
1  .-2,-, 3 


rCAUAN  SfNAIUANCL 
DMAZaO  VBNDRiAMIN- 
CAIiJeOl  ^  VENICE. 


EoyPTIAN-FRONT  OF  TE-MPLL. 


in  the  Greek  Doric  this 
consists  of  the  annulets 
immediately  below  the 
abacus ;  in  the  other 
orders,  the  necking  which 
divides  the  shaft  from 
the  cap. 

CONSONANCE 

"As  is  the  small,  so  is 
the  great"  is  a  perpetually 
recurring  phrase  in  the  lit- 
erature of  theosophy,  and 
naturally  so,  for  it  is  a 
succint  statement  of  a 
fundamental  and  far- 
reaching  truth.  The  scien- 
tist recognizes  it  now  and 
then,  and  here  and  there, 
but  the  occultist  trusts  it 
always  and  utterly.  To 
him  the  microcosm  and 
the  macrocosm  are  one 
and  the  same  in  essence, 
and  the  forth-going  im- 
pulse which  calls  a  uni- 
verse into  being  and  the  indrawing  impulse  which  extinguishes  it  again,  each 
lasting  millions  of  years,  are  echoed  and  repeated  in  the  inflow  and  outflow 
of  the  breath  through  the  nostrils,  in  nutrition  and  excretion,  in  daily  activity 
and  nightly  rest,  in  that  longer  day  which  we  name  a  lifetime,  and  that  longer 
rest  in  Devachan,  and  so  on,  up  and  up  and  up,  and  forever  and  ever 
and  ever. 

In  the  same  way,  in  nature,  a  thing  is  echoed  and  repeated  throughout 
its  parts.  Each  leaf  on  a  tree  is  itself  a  tree  in  miniature,  each  blossom  a 
modified  leaf ;  every  vertebrate  animal  is  a  complicated  system  of  spines ;  the 
ripple  is  the  wave  of  a  larger  wave,  and  that  larger  wave  is  part  of  the  ebbing 
and  flowing  tide.    In  music  this  law  is  illustrated  in  the  return  of  the  tonic 


I  FRENCH  RENAiyJANCE-CHA£AU 


BMAZZODAWOUNlFLOItENCf  DB  BEAUM&JNIb. 


23 


Ill 


CHANGELESS  CHANGE 


37 


THE.  LAW  OF  CCNSONANCL:  RjLPLTITION  ^A/ITH  VARIATION 

THE/  DOML-  OF  THE        TH£  SMALL  DOMES 
GCTHEORAbOF        i  PBEPAEM-THL  EYLFOib 
PIORtNCL.l  THE  dRfcAT  DOMB 


(  CORINTHIAN  CAPITAL  AND 
_J  BNTA5LATUE£,  SHQNA^INQ 
COEJbLSFONDLNCE  bhTWI^M 
THBIRJ  VARIOVS  PARTS. 


TH&  BEAD  AND  ILLEb 
ECHO  THE-  EXjG  AND 
TONGUE; 


THB  CHANNELED  TEJ- 
GLYPHS  AIOVE  ECHO 
THE  COLUMNS  bBlXV^ 


24 


to  itself  in  the  octave,  and  its  partial  return  in  the  dominant ;  also,  in  a  more 
extended  sense,  in  the  repetition  of  a  major  theme  in  the  minor,  or  in  the 
treble  and  again  in  the  bass,  with  modifications,  perhaps,  of  time  and  key.  In 
the  art  of  painting  the  law  is  exemplified  in  the  repetition  with  variation  of 
certain  colors  and  combinations  of  lines  in  different  parts  of  the  same  picture, 
so  disposed  as  to  lead  the  eye  to  some  focal  point.  Every  painter  knows  that 
any  important  color  in  his  picture  must  be  echoed,  as  it  were,  in  different 
places,  for  harmony  of  the  whole. 

In  the  drama  the  repetition  of  a  speech,  or  of  an  entire  scene,  but  under 
circumstances  which  give  it  a  different  meaning,  is  often  very  effective,  as 
when  Gratiano,  in  the  trial  scene  of  The  Merchant  of  Venice  taunts  Shylock 
with  his  own  words,  "A  Daniel  come  to  judgment!"  or,  as  when,  in  one  of 
the  later  scenes  of  As  You  Like  It,  an  earlier  scene  is  repeated,  but  with 
Rosalind  speaking  in  her  proper  person  and  no  longer  as  the  boy  Ganymede. 

These  recurrences,  these  inner  consonances,  these  repetitions  with  varia- 
tions are  common  in  architecture  also.    The  channeled  triglyphs  of  a  Greek 


38 


THE  BEAUTIFUL  NECESSITY 


III 


THE  DAW  a^ 
00N30NANCE 


ONE  EAY  OF  THE 
"ANQELCHaRSQP 
LINO0lKGAn£DRAL 


M 


Doric  frieze  echo  the  fluted  columns 
below  (Illustration  24).  The  balus- 
trade which  crowns  a  colonnade  is 
a  repetition,  in  some  sort,  of  the 
colonnade  itself.  The  modillions  of 
a  Corinthian  cornice  are  but  elabor- 
ate and  embellished  dentils.  Each 
pinnacle  of  a  Gothic  cathedral  is  a 
little  tower  with  its  spire.  As  Ruskin 
has  pointed  out,  the  great  vault  of 
the  cathedral  nave,  together  with  the 
pointed  roof  above  it,  is  repeated  in 
the  entrance  arch  with  its  gable,  and 
the  same  two  elements  appear  in 
every  statue-enshrining  niche  of  the 
doorway.  In  Classic  architecture,  as  has  been  shown,  instead  of  the  pointed 
arch  and  gable,  the  column  and  entablature  everywhere  recur  under  different 


■^ 


1 


THE  ^AMfi  MOTIF 
RfiPEATHD  WITH 
\AR;IATlONS— -^ 


25 


THB  LAW  OF  CONSONANCE!  R,EPETITION;^i/^  VARIATION 

\Mii/  iTiiT      A 


^^ 


CHATEAU   MAINTE;NON.~THE;  OBNTRAL  PAVIDION  \A/1TH  IT^TWQ 
TUR)R;E/TS  ECHOES  THE  ENTiafc  FACADE  WITH  ITS  TWO  TOWER^S 


26 


Ill 


CHANGELESS  CHANGE 


39 


THE  LAW  OF 
OONSONANCE 


forms.  The  minor  domes  which  flank  the  great  dome  of  the  cathedral  of 
Florence  enhance  and  reinforce  the  latter,  and  prepare  the  eye  for  a  climax 
which  would  otherwise  be  too  abrupt.  The  central  pavilion  of  the  Chateau 
Maintenon,  with  its  two  turrets,  echoes  the  entire  fagade  with  its  two  towers. 
Like  the  overture  to  an  opera,  it  introduces  themes 
which  find  a  more  extended  development  elsewhere 
(Illustration  26). 

This  law  of  Consonance  is  operative  in  archi- 
tecture more  obscurely  in  the  form  of  recurring 
numerical  ratios,  identical  geometrical  determining 
figures,  parallel  diagonals,  and  the  like,  which  will 
be  discussed  in  a  subsequent  essay.  It  has  also  to 
do  with  style  and  scale,  the  adherence  to  sub- 
stantially one  method  of  construction  and  manner 
of  ornament,  just  as  in  music  the  key,  or  chosen 
series  of  notes  may  not  be  departed  from  except 
through  proper  modulations,  or  in  a  specific  manner. 

Thus  it  is  seen  that  in  a  work  of  art,  as  in  a  piece 
of  tapestry,  the  same  thread  runs  through  the  web,  but  goes  to  make  up 
different  figures.  The  idea  is  deeply  theosophic:  one  life,  many  manifesta- 
tions; hence,  inevitably,  echoes,  resemblances — Consonance. 


PATffiRN  FROM  A; 
(DIONIAL  5EDSP2£AD 


27 


DIVERSITY  IN  MONOTONY 
Another  principle  of  natural  beauty,  closely  allied  to  the  foregoing,  its 
complement,  as  it  were,  is  that  of  Diversity  in  Monotony — not  identity,  but 
difference.  It  shows  itself  for  the  most  part  as  a  perceptible  and  piquant 
variation  between  individual  units  belonging  to  the  same  class,  type,  or 
species. 

No  two  trees  put  forth  their  branches  in  just  the  same  manner,  and  no 
two  leaves  from  the  same  tree  exactly  correspond ;  no  two  persons  look  alike, 
though  they  have  similar  members  and  features ;  even  the  markings  on  the 
skin  of  the  thumb  are  different  in  every  human  hand.    Browning  says, 
"As  like  as  a  hand  to  another  hand ! 
Whoever  said  that  foolish  thing. 
Could  not  have  studied  to  understand — " 
Now  every  principle  of  natural  beauty  is  but  the  presentment  of  some 
occult  law,  some  theosophical  truth,  and  this  law  of  Diversity  in  Monotony  is 


40 


THE  BEAUTIFUL  NECESSITY 


III 


THE  LAW  OF  DIVERSITY  IN  MONOTONY 
IPUUUOOT3U 


jDUCJUDTJUOqi 


Q 


ORKAMENlS 


'CONTINUED 


^ 


OIU^AMEOTJIIIiPcoNTlNUED 


UUOUlXJOl 


ORNAMElNT 


^B 

THR£E  PANELS  OP  DAS£A* 


s 

iOi 


DETAILS  FRDMTHH 
TEMPLE  OF  APOUD 
NEAl^^  MILETUS'--' 


28 


the  presentment  of  the  truth  that  identity  does  not  exclude  individuality. 
The  law  is  binding,  yet  the  will  is  free:  all  men  are  brothers,  bound  by  the 
ties  of  brotherhood,  yet  each  is  unique,  a  free  agent,  and  never  so  free  as 


Ill 


CHANGELESS  CHANGE 


41 


THE/  LAW  OF  DIVE^RSITY  IN  MCS^IOTONY.    exempufim)  in  thI/  lowwj/  ascadij  of  the.  pisa  G«rHM«AU 


FEOM  PEOf  tSSOa  OOOOYXAK/S  JUEVEV  Of  THL  SOUTH  WALL  OP  THE  PISA  CATHtDEAL.  JHOVVWO  VABIATICN  IN  HEIOHTJ- 
AND  VVIDTHJ  OP  THhABjCHli  Ct  THI.  ASCADE/.  AND  THE)  DIP  OF  THE.  H0EJ20NTAL  STRiNO  COUR.SI,  IMMtDlATLLY  Ar>OVL~- 


when  most  bound  by  the  Good  Law.  This  truth  nature  beautifully  pro- 
claims, and  art  also.  In  architecture  it  is  admirably  exemplified  in  the 
metopes  of  the  Parthenon  frieze:  seen  at  a  distance  these  must  have 
presented  a  scarcely  distinguishable  texture  of  sunlit  marble  and  cool  shadow, 
yet  in  reality,  each  is  a  separate  work  of  art.  So  with  the  capitals  of  the 
columns  of  the  wonderful  sea-arcade  of  the  Venetian  Ducal  palace :  alike  in 
general  contour  they  differ  widely  in  detail,  and  unfold  a  Bible  story.  In 
Gothic  cathedrals,  in  Romanesque  monastery  cloisters,  a  teeming  variety  of 
invention  is  hidden  beneath  apparent  uniformity.  The  gargoyles  of  Notre 
Dame  make  similar  silhouettes  against  the  sky,  but  seen  near  at  hand,  what 
a  menagerie  of  monsters !  The  same  spirit  of  controlled  individuality,  of 
liberty  subservient  to  the  law  of  all,  is  exemplified  in  the  bases  of  the  columns 
of  the  temple  of  Apollo  near  Mitelus, — each  one  a  separate  masterpiece  of 
various  ornamentation  adorning  an  estabHshed  architectural  form  (Illus- 
tration 28). 

The  builders  of  the  early  Italian  churches,  instinctively  obeying  this  law 
of  Diversity  in  Monotony,  varied  the  size  of  the  arches  in  the  same  arcade 
(Illustration  29),  and  that  this  was  an  effect  of  art  and  not  of  accident 
or  carelessness  Ruskin  long  ago  discovered,  and  the  Brooklyn  Institute 
surveys  have  amply  confirmed  his  view.  Although  by  these  means  the  build- 
ers of  that  day  produced  effects  of  deceptive  perspective,  of  subtle  concord 
and  contrast,  their  sheer  hatred  of  monotony  and  meaningless  repetition  may 
have  led  them  to  diversify  their  arcades  in  the  manner  described,  for  a 
rigidly  equal  and  regular  division  lacks  interest  and  vitality. 


BALANCE 
If  one  were  to  establish  an  axial  plane  vertically  through  the  center  of  a 


42  THE  BEAUTIFUL  NECESSITY  iii 

tree,  in  most  cases  it  would  be  found  that  the  masses  of  foliage,  however 
irregularly  shaped  on  either  side  of  such  an  axis,  just  about  balanced  one 
another.  Similarly,  in  all  our  bodily  movements,  for  every  change  of 
equilibrium  there  occurs  an  opposition  and  adjustment  of  members  of  such 
a  nature  that  an  axial  plane  through  the  center  of  gravity  would  divide  the 
body  into  two  substantially  equal  masses,  as  in  the  case  of  the  tree.  This 
physical  plane  law  of  Balance,  shows  itself  for  the  most  part  on  the  higher 
planes,  as  the  law  of  Compensation,  whereby,  to  the  vision  of  the  occultist, 
all  accounts  are  "squared,"  so  to  speak.  It  is,  in  effect,  the  law  of  Justice, 
aptly  symbolized  by  the  scales. 

The  law  of  Balance  finds  abundant  illustration  in  art :  in  music  by  the 
opposition,  the  answering,  of  one  phrase  by  another  of  the  same  length  and 
elements,  but  involving  a  different  succession  of  intervals ;  in  painting  by  the 
disposition  of  masses  in  such  a  way  that  they  about  equalize  one  another,  so 
that  there  is  no  sense  of  "strain"  in  the  composition. 

In  architecture  the  common  and  obvious  recognition  of  the  law  of 
Balance  is  in  the  symmetrical  disposition  of  the  elements,  whether  of  plan 
or  of  elevation,  on  either  side  of  axial  lines.  A  far  more  subtle  and  vital 
exhibition  of  the  law  occurs  when  the  opposed  elements  do  not  exactly 
match,  but  differ  from  one  another,  as  in  the  case  of  the  two  towers  of 
Amiens,  for  example.  This  sort  of  balance  may  be  said  to  be  characteristic 
of  Gothic,  as  symmetry  is  characteristic  of  Classic  architecture. 

RHYTHMIC  CHANGE 

There  is  in  nature  a  universal  tendency  towards  refinement  and  com- 
pactness of  form  in  space,  or  contrariwise,  towards  increment  and  diffusion ; 
and  this  manifests  itself  in  time  as  acceleration  or  retardation.  It  is  governed, 
in  either  case,  by  an  exact  mathematical  law,  like  the  law  of  falling  bodies. 
It  shows  itself  in  the  widening  circles  which  appear  when  one  drops  a  stone 
in  still  water,  in  the  convolutions  of  shells,  in  the  branching  of  trees,  and 
the  veining  of  leaves ;  the  diminution  in  the  size  of  the  pipes  of  an  organ 
illustrates  it,  and  the  spacing  of  the  frets  of  a  guitar.  More  and  more  science 
is  coming  to  recognize,  what  theosophy  has  ever  affirmed,  that  the  spiral 
vortex,  which  so  beautifully  illustrates  this  law,  both  in  its  time  and  its  space 
aspects,  is  the  universal  archetype,  the  pattern  of  all  that  is,  has  been,  or  will 
be,  since  it  is  the  shape  assumed  by  the  ultimate  physical  atom,  and  the  ulti- 
mate physical  atom  is  the  physical  cosmos  in  miniature. 


Ill  CHANGELESS  CHANGE  43 

This  Rhythmic  Diminution  is  everywhere :  it  is  in  the  eye  itself,  for 
any  series  of  mathematically  equal  units,  such,  for  example,  as  the  columns 
and  intercolumnations  of  a  colonnade,  become,  when  seen  in  perspective, 
rhythmically  unequal,  diminishing  according  to  the  universal  law.  The 
entasis  of  a  Classic  column  is  determined  by  this  law,  the  spirals  of  the 
Ionic  volute,  the  annulets  of  the  Parthenon  cap,  obey  it  (Illustration  30). 

In  recognition  of  the  same  principle  of  Rhythmic  Diminution  a  building 
is  often  made  to  grow,  or  to  appear  to  grow  lighter,  more  intricate,  finer, 
from  the  ground  upwards;  an  end  attained  by  various  devices,  one  of  the 
most  common  being  the  employment  of  the  more  attenuated  and  highly 
ornamented  orders  above  the  simpler  and  sturdier,  as  in  the  Roman  Colos- 
seum, or  in  the  Palazzo  Uguccioni,  in  Florence,  to  mention  only  two 
examples  out  of  a  great  number.  In  the  Riccardi  Palace  an  effect  of  increas- 
ing refinement  is  obtained  by  diminishing  the  boldness  of  the  rustication 
of  the  ashlar  in  successive  stories ;  in  the  Farnese,  by  the  gradual  reduction 
of  the  size  of  the  angle  quoins  (Illustration  30).  In  an  Egyptian  pylon  it  is 
achieved  most  simply  by  battering  the  wall ;  in  a  Gothic  cathedral  most  elab- 
orately, by  a  kind  of  segregation,  or  breaking  up,  analogous  to  that  which  a 
tree  undergoes, — the  strong,  relatively  unbroken  base  corresponding  to  the 
trunk,  the  diminishing  buttresses  to  the  tapering  limbs,  and  the  multitude  of 
delicate  pinnacles  and  crockets,  to  the  outermost  branches  and  twigs,  seen 
against  the  sky. 

RADIATION 

The  final  principle  of  natural  beauty  to  which  the  author  would  call 
attention  is  the  law  of  Radiation,  which  is,  in  a  manner,  a  return  to  the 
first,  the  law  of  Unity.  The  various  parts  of  any  organism  radiate  from,  or 
otherwise  refer  back  to  common  centers,  or  foci,  and  these  to  centers  of 
their  own.  The  law  is  represented  in  its  simplicity  in  the  star  fish,  in  its 
complexity  in  the  body  of  man ;  a  tree  springs  from  a  seed,  the  solar  system 
centers  in  the  sun. 

The  idea  here  expressed  by  the  term  radiation  is  a  familiar  one  to  all 
students  of  theosophy.  The  Logos  radiates  his  life  and  light  throughout  his 
universe,  bringing  into  activity  a  host  of  entities  which  become  themselves 
radial  centers;  these  generate  still  others,  and  so  on  endlessly.  This  princi- 
ple, like  every  other,  patiently  publishes  itself  to  us,  unheeding,  everywhere 
in  nature,  and  in  all  great  art  as  well;  it  is  a  law  of  optics,  for  example, 


44 


THE  BEAUTIFUL  NECESSITY 


III 


THL  h?W  OF  RHYTHMIC  DIMINUTION 

ANGL&  QUOINS  OP  THE  EARWE.SE.  ENLACE. 
^^  THIRD  STC«y 


J 


SHOWING  DIMINUTION  IN  EACH 


i  SUCCEEDING  STORjY. 


SECOND  STOBY 


firjSt  story 


'<l^ 


*A'  EiNIAILCrED. 


METHOD  OF  E-STAB 
LISHTNG  BNTASrS 
QEACOLUMN 


:-Tz-.-A. 


^ 1 

ANNULET^"^    ^- ■■ 

UNDEJS/NEATH  ECfflNUS'QF 

GAPS  OF  PAIbTHE-NON 


WCSVE-BAKD 


>    I 


SHELL 


ANGLt  QUOINS  OP  THE-  1ST 
STORY  OF  THE,  FAI&NE$& 
BMAC£  AT  EjQME. 


that  all  straight  lines  having  a  common  direction  if  sufficiently  prolonged 
appear  to  meet  in  a  point,  i.  e.,  radiate  from  it  (Illustration  31).  Leonardo 
da  Vinci  employed  this  principle  of  perspective  in  his  Last  Supper  to  draw 
the  spectator's  eye  to  the  picture's  central  figure,  the  point  of  sight  towards 


Ill 


CHANGELESS  CHANGE 


45 


which  the  lines  of  the  walls  and  ceiling  con- 
verge centering  in  the  head  of  Christ.  Puvis 
de  Chavannes,  in  his  Boston  Library  decora- 
tion, leads  the  eye,  by  a  system  of  triangula- 
tion,  to  the  small  figure  of  the  Genius  of 
Enlightenment  above  the  central  door  (Illus- 
tration 32)  ;  and  Ruskin,  in  his  Elements  of 
Drawing,  has  shown  how  artfully  Turner 
arranged  some  of  his  composition  to  attract 
attention  to  a  focal  point. 

This  law  of  Radiation  enters  largely  into 
architecture.    The  Colosseum,  based  upon  the 


OmVirHT  QP  SANTA  MARIA  I3E:UJ?  QRAZJE!   AT  MILAN 


^TH^  qi^KIU^^  OF'  ^NLIQHTI^NMI^NT  AND  Tffi  MUS^S  Chavannes 

THE  lAW  OF  imDlATION  IN  PAJNTINQ" 


32 


46 


THE  BEAUTIFUL  NECESSITY 


III 


THE  L/WOF  l^^DIATION 
ILLUSTMTED  IN  NATURE 


MAPLE 


ellipse,    a    figure    generated    from    two 

points,  or  foci,  and  the  Pantheon,  based 

upon  the  circle,  a  figure  generated  from 

a  single  center,  are   familiar  examples. 

The  distinctive  characteristic  of  Gothic 

construction,  the  concentration  or  focal- 

ization  of  the  weight  of  the  vaults  and 

arches  at  certain  points,  is  another  illus- 
tration of  the  same  principle  applied  to 

architecture,   beautifully   exemplified   in 

the   semi-circular   apse   of   a   cathedral, 

where  the  lines  of  the  plan  converge  to 

a  common  center,  and  the  ribs  of  the 

vaulting  meet  upon  the  capitals  of  the 

piers  and  columns,   seeming  to  radiate 

thence  to  still  other  centers  in  the  loftier 

vaults   which   finally   meet   in   a   center 

common  to  all. 

The  tracery  of  the  great  roses  high 

up  in  the  fagades  of  the  cathedrals  of  33 

Paris  and  of   Amiens   illustrate   Radiation, — in   the   one   case   masculine: 

straight,  angular,  direct;  in  the  other  feminine:  curved,  flowing,  sinuous. 

The  same  Beautiful 
Necessity  determined  the 
characteristics  of  much 
of  the  ornament  of  wide- 
ly separated  styles  and 
periods :  the  Egyptian 
lotus,  the  Greek  honey- 
suckle, the  Roman  acan- 
thus, Gothic  leaf  work — 
to  snatch  at  random  four 
blossoms  from  the  sheaf 
of  time.  The  radial 
principle  still  inherent  in 
the  debased  ornament  of 
the  late  Renaissance 


LAND  CRAb 


SiiOW  asVSTAL 


WHERb  ERNE5T 
THOMPSON  SETCN 


-^>^r<>^ 


THE  AKT  ANAT- 
>        ■  -<     ■       'i^a.-T— ""^tj.   i     OMYCF ANIMALS 


THE  IjAW5  of  EiiADlATION  AhfD  OF  R.HYTHM1G 
DIMINUTION  ILLUSTRATED  BV  A  PEAOOGK'S  TJAIN 


34 


Ill 


CHANGELESS  CHANGE 


47 


THE  L/^A/  OF  RADIATION 


FRENCH   RENAISSANCE         BYZ-ANTINE. 


35 


gives  that  ornament  a  unity, 
a  coherence,  and  a  kind  of 
beauty  all  its  own  (Illustra- 
tion 35). 

Such  are  a  few  of  the 
more  obvious  laws  of  natural 
beauty  and  their  application 
to  the  art  of  architecture. 
The  list  is  by  no  means  ex- 
hausted, but  it  is  not  the 
multiplicity  and  diversity  of 
laws  which  it  is  important  to 
keep  in  mind,  so  much  as 
their  essential  unity  and  co-ordination,  for  they  are  but  different  aspects  of 
the  One  Law,  that  whereby  the  Logos  manifests  himself  in  time  and  space. 
A  brief  recapitulation  will  serve  to  make  this  correlation  plain,  and  at  the 
same  time  fix  what  has  been  written  more  firmly  in  the  reader's  mind. 

First  comes  the  law  of  Unity;  then,  since  every  unit  is,  in  its  essence, 
twofold,  there  is  the  law  of 
Polarity;  but  this  duality  is 
not  static,  but  dynamic,  the 
two  parts  acting  and  react- 
ing upon  one  another  to 
produce  a  third,  hence  the 
law  of  Trinity.  Given  this 
third  term,  and  the  innumer- 
able combinations  made  pos- 
sible by  its  relations  to  and 
reaction  upon  the  original 
pair,  the  law  of  Multiplicity 
in  Unity  naturally  follows,  as  does  the  law  of  Consonance,  or  repetition, 
since  the  primal  process  of  differentiation  tends  to  repeat  itself,  and  the 
original  combination  to  reappear, — but  to  reappear  in  changed  form,  hence 
the  law  of  Diversity  in  Monotony.  The  law  of  Balance  is  seen  to  be  but  a 
modification  of  the  law  of  Polarity,  and  since  all  things  are  waxing  and 
waning,  there  is  the  law  whereby  they  wax  and  wane,  that  of  Rhythmic 
Change.    Radiation  rediscovers  and  reaffirms,  even  in  the  utmost  complexity. 


48  THE  BEAUTIFUL  NECESSITY  iii 

that  essential  and  fundamental  unity  from  which  complexity  was  wrought. 

Everything,  beautiful  or  ugly,  obeys  and  illustrates  one  or  another  of 
these  laws,  so  universal  are  they,  so  inseparably  attendant  upon  every  kind 
of  manifestation  in  time  and  space.  It  is  the  number  of  them  which  finds 
illustration  within  small  compass,  as  it  were,  and  the  aptness  and  complete- 
ness of  such  illustration  which  makes  for  beauty,  because  beauty  is  the  fine 
flower  of  a  sort  of  sublime  ingenuity.  A  work  of  art  is  nothing  if  not  artful : 
like  an  acrostic,  the  more  different  ways  it  can  be  read — up,  down,  across, 
from  right  to  left  and  from  left  to  right — the  better  it  is,  other  things  being 
equal.  This  statement,  of  course,  may  be  construed  in  such  a  way  as  to 
appear  absurd;  what  is  meant  is  simply  that  the  more  a  work  of  art  is 
freighted  and  fraught  with  meaning  beyond  meaning,  the  more  secure  its 
immortality,  the  more  powerful  its  appeal.  For  enjoyment,  it  is  not  neces- 
sary that  all  these  meanings  should  be  fathomed,  it  is  only  necessary  that 
they  should  be  felt. 

Consider  for  a  moment  the  manner  in  which  Leonardo  da  Vinci's  Last 
Supper,  an  acknowledged  masterpiece,  conforms  to  every  one  of  the  laws  of 
beauty  enumerated  above  (Illustration  32).  It  illustrates  the  law  of  Unity 
in  that  it  movingly  portrays  a  single  significant  episode  in  the  life  of  Christ. 
The  eye  is  led  to  dwell  upon  the  central  personage  of  this  drama  by  many 
artful  expedients:  the  visible  part  of  the  figure  of  Christ  conforms  to  the 
lines  of  an  equilateral  triangle  placed  exactly  in  the  center  of  the  picture,  the 
figure  is  separated  by  a  considerable  space  from  the  groups  of  the  disciples 
on  either  hand,  and  stands  relieved  against  the  largest  parallelogram  of  light, 
and  the  vanishing  point  of  the  perspective  is  in  the  head  of  Christ,  at  the 
apex,  therefore,  of  the  triangle.  The  law  of  Polarity  finds  fulfillment  in  the 
complex  and  flowing  lines  of  the  draped  figures  contrasted  with  the  simple 
parallelogram  of  the  cloth-covered  table,  and  the  severe  architecture  of  the 
room;  the  law  of  Trinity  is  exemplified  in  the  three  windows,  and  in  the 
subdivision  of  the  twelve  figures  of  the  disciples  into  four  groups  of  three 
figures  each.  The  law  of  Consonance  appears  in  the  repetition  of  the  hori- 
zontal lines  of  the  table  in  the  ceiling  above;  and  in  the  central  triangle 
before  referred  to,  continued  and  echoed,  as  it  were,  in  the  triangular  sup- 
ports of  the  table  visible  underneath  the  cloth.  The  law  of  Diversity  in 
Monotony  is  illustrated  in  the  varying  disposition  of  the  heads  of  the  figures 
in  the  four  groups  of  three;  the  law  of  Balance  in  the  essential  symmetry 
of  the  entire  composition;  the  law  of  Rhythmic  Change  in  the  diminishing 


Ill  CHANGELESS  CHANGE  49 

of  the  wall  and  ceiling  spaces,  and  the  law  of  Radiation  in  the  convergence 
of  all  the  perspective  lines  to  a  single  significant  point. 

To  illustrate  further  the  universality  of  these  laws,  consider  now  their 
application  to  a  single  work  of  architecture :  the  Taj  Mahal,  one  of  the  most 
beautiful  buildings  of  the  world  (Illustration  36).  It  is  a  unit,  but  twofold, 
for  it  consists  of  a  curved  part  and  an  angular  part,  roughly  figured  as  an 
inverted  cup  upon  a  cube;  each  of  these  (seen  in  parallel  perspective,  at  the 
end  of  the  principal  vista)  is  threefold,  for  there  are  two  sides  and  a  central 
parallelogram,  and  two  lesser  domes  flank  the  great  dome.  The  composition 
is  rich  in  consonances,  for  the  side  arches  echo  the  central  one,  the  sub- 
ordinate domes,  the  great  dome,  and  the  lanterns  of  the  outstanding  minarets 
repeat  the  principal  motif.  Diversity  in  Monotony  appears  abundantly  in 
the  ornament,  which  is  intricate  and  infinitely  various ;  the  law  of  Balance  is 
everywhere  operative  in  the  symmetry  of  the  entire  design.  Rhythmic 
Change  appears  in  the  tapering  of  the  minarets,  the  outlines  of  the  domes 
and  their  mass  relations  to  one  another;  and  finally,  the  whole  effect  is  of 
radiation  from  a  central  point,  of  elements  disposed  on  radial  lines. 

It  would  be  fatuous  to  contend  that  the  prime  object  of  a  work  of 
architecture  is  to  obey  and  illustrate  these  laws.  The  prime  object  of  a 
work  of  architecture  is  to  fulfill  certain  definite  conditions  in  a  practical, 
economical,  and  admirable  way,  and  in  fulfilling  to  express  as  far  as 
possible  these  conditions  and  the  manner  of  their  fulfilment.  The  architect 
who  is  also  an  artist,  however,  will  do  this  and  something  beyond.  Working 
for  the  most  part  unconsciously,  harmoniously,  joyfully,  his  building  will 
obey  and  illustrate  natural  laws — these  laws  of  beauty — and  to  the  extent  it 
does  so,  it  will  be  a  work  of  art,  for  art  is  the  method  of  nature  carried  into 
those  higher  regions  of  thought  and  feeling  which  man  alone  inhabits : 
regions  which  it  is  one  of  the  missions  of  theosophy  to  explore. 


IV 
THE  BODILY  TEMPLE 

CARLYLE  says :  "There  is  but  one  temple  in  the  world,  and  that  is  the 
body  of  man."  If  the  body  is,  as  he  declares,  a  temple,  it  is  not  less 
true  that  a  temple  or  any  work  of  architectural  art  is  a  larger  body 
which  man  has  created  for  his  uses,  just  as  the  individual  self  is  housed 
within  its  stronghold  of  flesh  and  bones.  Architectural  beauty,  like  human 
beauty,  depends  upon  the  proper  subordination  of  parts  to  the  whole,  the 
harmonious  interrelation  between  these  parts,  the  expressiveness  of  each  of 
its  function  or  functions,  and  when  these  are  many  and  diverse,  their  recon- 
«  cilement  one  with  another.  This  being  so,  a  study  of  the  human  figure  with  a 
view  to  analyzing  the  sources  of  its  beauty  cannot  fail  to  be  profitable.  Pur- 
sued intelligently,  such  a  study  will  stimulate  the  mind  to  a  perception  of 
those  simple  yet  subtle  laws  according  to  which  nature  everywhere  works,  and 
it  will  educate  the  eye  in  the  finest  known  school  of  proportion,  training  it  to 
distinguish  minute  differences,  in  the  same  way  that  the  hearing  of  good 
music  cultivates  the  ear. 

Those  principles  of  natural  beauty  which  formed  the  subject  of  the  two 
preceding  essays  are  all  exemplified  in  the  ideally  perfect  human  figure. 
Though  essentially  a  unit,  there  is  a  well  marked  division  into  right  and 
left.  "Hands  to  hands,  and  feet  to  feet,  in  one  body  grooms  and  brides." 
There  are  two  arms,  two  legs,  two  ears,  two  eyes,  and  two  lids  to  each  eye : 
the  nose  has  two  nostrils,  the  mouth  has  two  lips.  Moreover,  the  terms  of 
such  pairs  are  masculine  and  feminine  with  regard  to  each  other,  one  being 
active  and  the  other  passive.  Owing  to  the  great  size  and  one-sided  position 
of  the  liver,  the  right  half  of  the  body  is  heavier  than  the  left;  the  right 

[so] 


IV 


THE  BODILY  TEMPLE 


51 


r\ 


THB  IA\AA  OP  RHYTHMIC 

INTH/TAPBRING  BOD^ 
J     V]ME>$.  F1NQE/R)$  &  TOE^. 


37 


arm  is  usually  longer  and  more 

muscular  than  the  left;  the  right 

eye   is    slightly   higher   than   its 

fellow.     In  speaking  and  eating 

the  lower  jaw  and  under  lip  are 

active  and  mobile  with  relation 

to  the  upper;  in  winking  it  is 

the    upper   eyelid   which   is    the 

more    active.     That    "inevitable 

duality"  which  is  exhibited  in  the 

form  of  the  body  characterizes 

its  motions  also.     In  the  act  of 

walking  for  example,  a  forward 

movement  is  attained  by  means 

of   a   forward  and  a   backward 

movement  of  the  thighs  on  the  axis  of  the  hips ;  this  leg  movement  becomes 

twofold  again  below  the  knee,  and  the  feet  move  up  and  down  independently 

on  the  axis  of  the  ankle,     A  similar  progression  is  followed  in  raising  the 

arm  and  hand :  motion  is  communicated  first  to  the  larger  parts,  through 

them  to  the  smaller,  and  thence  to  the  extremities,  becoming  more  rapid  and 

complex  as  it  progresses,  so  that  all  free  and  natural  movements  of  the  limbs 
describe  invisible  lines  of  beauty  in  the  air.  Coexistent  with 
this  pervasive  duality,  there  is  a  threefold  division  of  the 
figure  into  trunk,  head,  and  limbs,  a  superior  trinity  of  head 
and  arms,  and  an  inferior  trinity  of  trunk  and  legs.  The 
limbs  are  divided  threefold  into  upper-arm,  forearm,  and 
hand ;  thigh,  leg,  and  foot.  The  hand  flowers  out  into 
fingers  and  the  foot  into  toes,  each  with  a  threefold  articula- 
tion; and  in  this  way  is  effected  that  transition  from  unity 
to  multiplicity,  from  simplicity  to  complexity,  which  ap- 
pears to  be  so  universal  throughout  nature,  and  of  which  a 
tree  is  the  perfect  symbol. 

The  body  is  rich  in  veiled  repetitions,  echoes,  conson- 
ances.    The  head  and  arms  are  in  a  sense  a  refinement 

upon  the  trunk  and  legs,  there  being  a  clearly  traceable  correspondence 

between  their  various  parts.     The  hand  is  the  body  in  little, — "Your  soft 

hand  is  a  woman  of  itself," — the  palm,  the  trunk ;  the  four  fingers,  the  four 


52 


THE  BEAUTIFUL  NECESSITY 


IV 


jTTrN.       n'HE/  CLENCHED  JIST  AND 
WV3       ^    THEW5il/E-EAND(3DMIi»JiM) 


SCALLOP  5HE,I/L 


THE.  HAND  OPE-N 


<■  NAUTILUS  5HM/L 


ANTE/FIX 
'<-THE  HAND  0D05ED 


A  COMPARISON  BE^TVA/^EN  THE  HAND.CLOXE'D 
AND  OPEN.  AND  THE  GEEEK  ANTEEIX.AND  SHE<LU 


39 

(Illustrations  37,  38).  Finally,  the  limbs 
the  fingers  from  a  point  in  the  wrist,  the 
toes  from  a  point  in  the  ankle.  The 
ribs  radiate  from  the  spinal  column  like 
the  veins  of  a  leaf  from  its  midrib  (Illus- 
tration 39). 

The  relation  of  these  laws  of  beauty 
to  the  art  of  architecture  has  been  shown 
already.  They  are  reiterated  here  only 
to  show  that  man  is  indeed  the  micro- 
cosm— a  little  world  fashioned  from  the 
same  elements  and  in  accordance  with 
the  same  Beautiful  Necessity  as  is  the 
greater  world  in  which  he  dwells.  When 
he  builds  a  house  or  temple  he  builds 
it  not  literally  in  his  own  image,  but 
according  to  the  laws  of  his  own  being, 
and  there  are  correspondences  not  alto- 
gether fanciful  between  the  animate  body 
of  flesh  and  the  inanimate  body  of  stone. 


limbs;  and  the  thumb,  the 
head;  each  finger  is  a  little 
arm,  each  finger  tip  a  little 
palm.  The  lips  are  the  lids  of 
the  mouth,  the  lids  are  the 
lips  of  the  eyes — and  so  on. 
The  law  of  rhythmic  diminu- 
tion is  illustrated  in  the  taper- 
ing of  the  entire  body  and  of 
the  limbs,  in  the  graduated 
sizes  and  lengths  of  the 
fingers  and  the  toes,  and  in 
the  successively  decreasing 
lengths  of  the  palm  and  of 
the  joints  of  the  fingers,  so 
that  in  closing  the  hand  the 
fingers  describe  natural  spirals 
radiate  as  it  were  from  the  trunk. 


A  CCMEAEISON"  E&TWEfcN  CrIOTTO'S 
GAMIANILE,  A  COLUMN  lEDM  TUB  D^R. 
THENQN,  AND  THE  HtHMAN  MQUM.— 


40 


IV 


THE  BODILY  TEMPLE 


S3 


THE  BODY  TOE  AKCHETVRE 
OF  SAGItED  EDIFICES  ^g^ 

feqOTHiC 
CHUSCH 


Do  we  not  all  of  us,  consciously  or 
unconsciously,  recognize  the  fact  of 
character  and  physiognomy  in  build- 
ings ?  Are  they  nc^,  to  our  imagina- 
tion, masculine  or  feminine,  winning 
or  forbidding — human,  in  point  of 
fact — to  a  greater  degree  that  any- 
thing else  of  man's  creating?  They 
are  this  certainly  to  the  true  lover 
and  student  of  architecture.  Seen 
from  a  distance,  the  great  French 
cathedrals  appear  like  crouching 
monsters,  half  beast,  half  human : 
the   two   towers    stand   like   a   man 

41 

and   a   woman,   mysterious   and 

gigantic,  looking  out  across  the  city  or  plain.    The  campaniles  of  Italy  rise 
above  the  churches  and  houses  like  the  sentinels  of  a  sleeping  camp, — nor  is 

their  strangely  human 


THE  KANDAEIYA         CHUKCH  CP  <ST. 
TEMPLE,  KHAJURAHO     OUEN  AT  ROUEN 


aspect  wholly  imaginary: 

these  giants  of  mountain 

and  campagna  have  eyes 

and  brazen  tongues ;  rising 

four  square,  story  above 

story,    with    a    belfry    or 

lookout,  like  a  head,  atop, 

their  likeness  to  a  man  is 

not  infrequently  enhanced 

by   a   certain   identity   of 

proportion :  of  ratio,  that 

is,  of  height  to  width — 

Giotto's    beautiful    tower 

is    an    example.     The 

caryatid   is   a   supporting 

^^  member  in  the  form  of  a 

woman;  in  the  Ionic  column  we  discern  her  stiffened,  like  Lot's  wife,  into  a 

pillar,  with  nothing  to  show  her  feminine  but  the  spirals  of  her  beautiful 

hair.     The  columns  which  uphold  the  pediment  of  the  Parthenon  are  as 


THg  VESICA  PlSaS  A^D  THE  PLAN  OF  CHAJJTKE'J' 


54 


THE  BEAUTIFUL  NECESSITY 


IV 


unmistakably  masculine:  the  ratio  of  their  breadth  to  their  height  is  the 
ratio  of  the  breadth  to  the  height  of  a  man  (Illustration  40). 

At  certain  periods  of  the  world's  history,  periods  of  mystical  enlighten- 
ment, men  have  been  wont  to  use  the  human  figure,  the  soul's  temple,  as  a 
sort  of  archetype  for  sacred  edifices  (Illustration  41),  The  colossi,  with 
calm,  inscrutable  faces,  which  flank  the  entrance  to  Egyptian  temples;  the 


PLAN  Ol^Cfflr 

OF  POITI£-K^.  FRANC 


AN  IVORyCAJ2VIK6 

OF  TTiEj  TWBU=TH 

CENTUEY 


riAN  OB  CXTHSDRALOP-  BEAUVAT^ 

fS^^™~I AGOTHIC CKTHhDZAL  THE.  SYMbOh 
wiNixjw,  TOiTiEJui^F  THE  50DY  OF  JhSUS  CHICIST-^^- 


great  bronze  Buddha  of  Japan,  v/ith  its  dreaming  eyes;  the  little  known 
colossal  figures  of  India — all  these  belong  scarcely  less  to  the  domain  of 
architecture  than  of  sculpture.  The  relation  above  referred  to,  however,  is  a 
matter  more  subtle  and  occult  than  mere  obvious  imitation  on  a  large  scale, 
being  based  upon  some  correspondence  of  parts,  or  similarity  of  propor- 
tions, or  both.  The  correspondence  between  the  innermost  sanctuary  or 
shrine  of  a  temple  and  the  heart  of  a  man,  and  between  the  gates  of  that 
temple  and  the  organs  of  sense  is  sufficiently  obvious,  and  a  relation  once 


IV 


THE  BODILY  TEMPLE 


55 


ALPHA 

NQEJTH  CBtEmAL  KXt 
SUN  aiSBJ— EAJT 

AP5E/  CdbAPSI^ 
CBOWN  CPTHOaNS 
HEAD 


DEOCIXfo 


NDKTH  TEiANSEn 
BIGHT  HAND 


CHaRj: 


PIAC£>OFPCN5 


MALE)  SACRED 
PILLAR'JACHIN" 


SOUTH  TEANStPT 
LEFT  HAND 


FEMALE  SAOLED 
riUAK>"5QA2,' 


WINL 


BREAD 


established,  the  idea  is  sus- 
ceptible of  almost  infinite  de- 
velopment. That  the  ancients 
proportioned  their  temples 
from  the  human  figure  is  no 
new  idea,  nor  is  it  at  all  sur- 
prising. The  sculpture  of  the 
Egyptians  and  the  Greeks  re- 
veals the  fact  that  they  studied 
the  body  abstractly,  in  its  ex- 
terior presentmeri^  It  is  clear 
that  the  rules  of  its  proportions 
must  have  been  established  for 
sculpture,  and  it  is  not  un- 
reasonable to  suppose  that  they 
became  canonical  in  architec- 
ture also.  Vitruvius  and  Al- 
berti  both  lay  stress  on  the  fact 
that  all  sacred  buildings  should 
be  founded  on  the  proportions 
of  the  human  body. 

In  France,  during  the  Mid- 
dle Ages,  a  Gothic  cathedral 
became,  at  the  hands  of  the  secret  masonic  guilds,  a  glorified  symbol  of 
the  body  of  Christ.  To  practical-minded  students  of  architectural  history, 
familiar  with  the  slow  and  halting  evolution  of  a  Gothic  cathedral  from  a 
Roman  basilica,  such  an  idea  may  seem  to  be  only  the  maunderings  of  a 
mystical  imagination,  a  theory  evolved  from  the  inner  consciousness,  entitled 
to  no  more  consideration  than  the  familiar  fallacy  that  the  vaulted  nave  of 
a  Gothic  church  was  an  attempt  to  imitate  the  green  aisles  of  a  forest.  It 
should  be  remembered,  however,  that  the  habit  of  the  thought  of  that  time 
was  mystical,  as  that  of  our  own  age  is  utilitarian  and  scientific;  and  the 
chosen  language  of  mysticism  is  always  an  elaborate  and  involved  symbolism. 
What  could  be  more  natural  than  that  a  building  devoted  to  the  worship 
of  a  crucified  Saviour  should  be  made  a  symbol,  not  of  the  cross  only,  but 
of  the  body  crucified  ? 

The  vesica  piscis   (a  figure   formed  by  the  developing  arcs   of   two 


SCXTTH  CELEmAJL,  POLE > 

SUN  SETS— WBST 

OMEGA 

THB  SYMBOLISM  OP  A  QOmiC  CATHEI)RAL 
PRiCM'^THE.  BQSICRUCIANSrHAKGRJWB  JBNNU^S 


44 


s^ 


THE  BEAUTIFUL  NECESSITY 


IV 


l^^% 


THB.  GEOMETTRICAL  BASIS  OF  THE  HUMAN  BIGUJ^E 

O 

n 


7^ 


^T£yIt>NUM 

BODV  i<S 
PUBIS 


-tHlGH  56 


J>EX3  Va 


^HE  ■•RE.LtATIQN'  OP  THE  HQIIRi&Tr) 
'r]£b$QUhS£>,'^H^  CIRCLE;.  AND  THE 


THE  PltOPpETlON^  OF  THE/ 
MQUaLAS  EiSTABU^HRD  £Y 
DOClDRi  RjIMMElt). 


45 

equilateral  triangles  having  common  side)  which  in 
so  many  cases  seems  to  have  determined  the  main 
proportion  of  a  cathedral  plan — the  interior  length 
and  the  width  across  the  transepts — appears  as  an 
aureole  around  the  figure  of  Christ  in  early  repre- 
sentations, a  fact  which  certainly  points  to  a  relation 
between  the  two  (Illustrations  42,  43).  A  curious 
little  book,  The  Rosicrucians,  by  Hargrave  Jen- 
nings, contains  an  interesting  diagram  which  well 
illustrates  this  conception  of  the  symbolism  of  a  cathedral.  A  copy  of  it  is 
here  given.  The  apse  is  seen  to  correspond  with  the  head  of  Christ,  the  north 
transept  to  his  right  hand,  the  south  transept  to  the  left  hand,  the  nave  to  the 
body,  and  the  north  and  south  towers  to  the  right  and  left  feet  respectively 
(Illustration  44). 

The  cathedral  builders  excelled  all  others  in  the  artfulness  with  which 
they  established  and  maintained  a  relation  between  their  architecture  and 
the  stature  of  a  man.     This  is  perhaps  one  reason  why  the  French  and 


IV 


THE  BODILY  TEMPLE 


57 


47 


English  cathedrals,  even  those  of 
moderate  dimensions,  are  more  truly 
impressive  than  even  the  largest  of 
the  great  Renaissance  structures, 
such  as  St.  Peter's,  in  Rome.  A 
gigantic  order  furnishes  no  true 
measure  for  the  eye:  its  vastness 
is  revealed  only  by  the  accident  of 
some  human  presence  which  forms 
a  basis  of  comparison.  That  archi- 
tecture is  not  necessarily  the  most 
awe-inspiring  which  gives  the  im- 
pression of  having  been  built  by 
giants  for  the  abode  of  pigmies;  like  the  other  arts,  architecture  is  highest 
when  it  is  most  human.  The  mediaeval  builders,  true  to  this  dictum,  em- 
ployed stones  Qf  a  size  proportionate  to  the  strength  of, a  man  working 
without  unusual  mechanical  aids;  the  great  piers  and  columns,  built  up  of 
many  such  stones,  were  commonly  subdivided  into  clusters,  and  the  circum- 
ference of  each  shaft  of  such  a  cluster  approximated 
the  girth  of  a  man;  by  this  device  the  mouldings  of 
the  base  and  the  foliation  of  the  caps  were  easily  kept 
in  scale.  Wherever  a  balustrade  occurred  it  was 
proportioned,  not  with  relation  to  the  height  of  the 
wall  or  column  below,  as  in  classic  architecture,  but 
with  relation  to  a  man's  stature. 

It  may  be  stated  as  a  general  rule  that  every  work 
of  architecture,  of  whatever  style,  should  have  some- 
where about  it  something  fixed  and  enduring  to  relate 
it  to  the  human  figure,  if  it  be  only  a  flight  of  steps 
in  which  each  one  is  the  measure  of  a  stride.  In  the 
Farnese,  the  Riccardi,  the  Strozzi,  and  many  another 
Italian  palace,  the  stone  seat  about  the  base  gives  scale 
to  the  building  because  the  beholder  knows  instinctively 
that  the  height  of  such  a  seat  must  have  same  relation 
to  the  length  of  a  man's  leg.  In  the  Pitti  palace  the 
balustrade  which  crowns  each  story  answers  a  similar 
purpose :  it  stands  in  no  intimate  relation  to  the  gigantic 


l*IGfURjE  DrviEEO 
EXSYPTtAN  CANON 


48 


58 


THE  BEAUTIFUL  NECESSITY 


IV 


TI£  :^aor  %Tffi  HEldHT 


nm  MEDIAEVAL  METHCD 
a?  ESJ^AWINQ  THE  PiQfDEE 


49 


arches  below,  but  is  of  a  height  convenient  for 

lounging  elbows.    The  door  to  Giotto's  cam- 
panile reveals  the  true  siie  of  the  tower  as 

nothing  else  could,  because  it  is  so  evidently 

related  to  the  human  figure  and  not  to  the 

great  windows  higher  up  in  the  shaft. 

The  geometrical  plane  figures  which  play 

the    most    important    part    in    architectural 

proportion  are  the  square,  the  circle  and  the 

triangle;  and  the  human  figure  is  intimately 

related  to  these  elementary  forms.    If  a  man 

stand   with   heels^ together,   and   arms   out- 
stretched horizontally  in  opposite  directions, 

he  will  be  inscribed,  as  it  were,   within  a 

square,  and  his  arms  will  mark,  with  fair 

accuracy,  the  base  of  an  inverted  equilateral 

triangle,  the  apex  of  which  will  touch  the 

ground  at  his  feet.    If  the  arms  be  extended  upward  at  an  angle,  and  the 

legs  correspondingly  separated,  the  extremities  will  touch  the  circumferences 

of  a  circle  having  its  center  in  the  navel  (Illustrations  45,  46). 

The  figure  has  been  variously  analyzed 
with  a  view  to  establishing  numerical 
ratios  between  its  parts  (Illustrations  47, 
48,  49).  Some  of  these  are  so  simple 
and  easily  remembered  that  they  have 
obtained  a  certain  popular  currency ;  such 
as  that  the  length  of  the  hand  equals  the 
length  of  the  face;  that  the  span  of  the 
horizontally  extended  arms  equals  the 
height;  and  the  well  known  rule  that 
twice  around  the  wrist  is  once  around 
the  neck,  and  twice  around  the  neck  is 
once  around  the  waist.  The  Roman 
architect,  Vitruvius,  writing  in  the  age 
of  Augustus  Caesar,  formulated  the  im- 
portant proportions  of  the  statues  of 
classical   antiquity,   and   except   that  he 


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50 


IV  THE  BODILY  TEMPLE  59 

makes  the  head  smaller  than  the  normal  (as  it  should  be  in  heroic  statuary), 
the  ratios  which  he  gives  are  those  to  which  the  ideally  perfect  male  figure 
should  conform.  Among  the  ancients  the  foot  was  probably  the  standard 
of  all  large  measurements,  being  a  more  determinate  length  than  that  of  the 
head  or  face,  and  the  height  was  six  lengths  of  the  foot.  If  the  head  be 
taken  as  a  unit,  the  ratio  becomes  i  :8,  and  if  the  face, — i  :io. 

Doctor  Rimmer,  in  his  Art  Anatomy,  divides  the  figure  into  four  parts, 
three  of  which  are  equal,  and  correspond  to  the  lengths  of  the  leg,  the  thigh 
and  the  trunk;  while  the  fourth  part,  which  is  two-thirds  of  one  of  these 
thirds,  extends  from  the  sternum  to  the  crown  of  the  head.  One  excellence 
of  such  a  divisioa  aside  from  its  simplicity,  consists  in  the  fact  that  it  may 
be  applied  to  the  face  as  well.  The  lowest  of  the  three  major  divisions 
extends  from  the  tip  of  the  chin  to  the  base  of  the  nose,  the  next  coincides 
with  the  height  of  the  nose  (its  top  being  level  with  the  eyebrows),  and  the 
last  with  the  height  of  the  forehead,  while  the  remaining  two-thirds  of  one 
of  these  thirds  represents  the  horizontal  projection  from  the  beginning  of  the 
hair  on  the  forehead  to  the  crown  of  the  head.  The  middle  of  the  three 
larger  divisions  locates  the  ears,  which  are  the  same  height  as  the  nose  (Illus- 
tration 45). 

Such  analyses  of  the  figure,  however  conducted,  reveal  an  all-pervasive 
harmony  of  parts,  between  which  definite  numerical  relations  are  traceable, 
and  an  apprehension  of  these  should  assist  the  architectural  designer  to 
arrive  at  beauty  of  proportion  by  methods  of  his  own,  not  perhaps  in  the 
shape  of  rigid  formulae,  but  present  in  the  consciousness  as  a  restraining 
influence,  acting  and  reacting  upon  the  mind  with  a  conscious  intention 
towards  rhythm  and  harmony.  By  means  of  such  exercises,  he  will  approach 
nearer  to  an  understanding  of  that  great  mystery,  the  beauty  and  significance 
of  numbers,  of  which  mystery  music,  architecture,  and  the  human  figure  are 
equally  presentments — considered,  that  is,  from  the  standpoint  of  the 
occultist. 


V 
LATENT  GEOMETRY 

THE  analysis  of  the  chemical  elements  by  means  of  clairvoyant  vision, 
undertaken  by  Mrs.  Besant  and  Mr.  Leadbeater,  and  lately  published 
to  the  world  in  Occult  Chemistry,  makes  plain  the  fact  that  units 
everywhere  tend  to  arrange  themselves  with  relation  to  certain  simple 
geometrical  solids,  among  which  are  the  tetrahedron,  the  cube,  and  the  sphere. 
This  process  gives  rise  to  harmony,  which  may  be  defined  as  the  relation 
between  parts  and  unity,  the  simplicity  latent  in  the  infinitely  complex,  the 
potential  complexity  of  that  which  is  simple.  Proceeding  to  things  visible 
and  tangible,  this  indwelling  harmony,  rhythm,  proportion,  which  has  its  basis 
in  geometry  and  number,  is  seen  to  exist  in  crystals,  flower  forms,  leaf 
groups,  and  the  like,  where  it  is  obvious;  and  in  the  more  highly  organized 
world  of  the  animal  kingdom,  also ;  though  here  the  geometry  is  latent  rather 
than  patent,  eluding,  though  not  quite  defying  analysis,  and  thus  augmenting 
beauty,  which,  like  a  woman,  is  alluring  in  proportion  as  she  eludes  (Illus- 
trations 51,  52,  53). 

By  the  true  artist,  in  the  crystal  mirror  of  whose  mind  the  universal 
harmony  is  focused  and  reflected,  this  secret  of  the  cause  and  source  of 
rhythm — that  it  dwells  in  a  correlation  of  parts  based  on  an  ultimate  sim- 
plicity— is  instinctively  apprehended.  A  knowledge  of  it  formed  part  of 
the  equipment  of  the  painters  who  made  glorious  the  golden  noon  of  pictorial 
art  in  Italy,  during  the  Renaissance.  The  problem  which  preoccupied  them 
was,  as  Symonds  says  of  Leonardo,  "to  submit  the  freest  play  of  form  to 
simple  figures  of  geometry  in  grouping."  Alberti  held  that  the  painter  should, 
above  all  things,  have  mastered  geometry,  and  it  is  known  that  the  study  of 
perspective  and  kindred  subjects  was  widespread  and  popular. 

[60] 


LATENT  GEOMETRY 


6i 


THL  HEXAGRAM  AND  EOUILATBRALTR,IANOLL  IN  NATURE 


^Now  cEsr>nAU 


HONI.Y  COMB 


THEEACE. 


FLL5H  FLY 


The  first  painter  who  dehberately 
rather  than  instinctively  based  his  com- 
position on  geometrical  principles  seems 
to  have  been  Fra  Bartolomeo,  in  his  Last 
Judgment,  in  the  church  of  St.  Maria 
Nuova,  in  Florence.  Symonds  says  of 
this  picture,  "Simple  figures — the  pyra- 
mid and  triangle,  upright,  inverted,  and 
interwoven  like  the  rhymes  of  a  sonnet 
— form  the  basis  of  the  composition. 
This  system  was 


53 


adhered  to  by  the 
Fratre  in  all  his 
subsequent  works"  (Illustration  54).  Raphael,  with 
that  power  of  assimilation  which  distinguishes  him 
among  men  of  genius,  learned  from  Fra  Bartolomeo 
this  method  of  disposing  figures  and  combining  them 
in  masses  with  almost  mathematical  precision.  It 
would  have  been  indeed  surprising  if  Leonardo  da 
Vinci,  in  whom  the  artist  and  the  man  of  science 
were  so  wonderfully  united,  had  not  been  greatly 
preoccupied  with  the  mathematics  of  the  art  of  paint- 
ing.   His  Madonna  of  the  Rocks,  and  Virgin  on  the 


62 


THE  BEAUTIFUL  NECESSITY 


Lap  of  Saint  Anne,  in  the  Louvre,  exhibit 
the  very  perfection  of  pyramidal  composition. 
It  is,  however,  in  his  masterpiece.  The  Last 
Supper,  that  he  combines  geometrical  sym- 
metry and  precision  with  perfect  naturalness 
and  freedom  in  the  grouping  of  individually 
interesting  and  dramatic  figures.  Michael 
Angelo,  Andrea  del  Sarto,  and  the  great 
Venetians,  in  whose  work  the  art  of  painting 
may  be  said  to  have  culminated,  recognized 
and  obeyed  those  mathematical  laws  of  com- 
position known  to  their  immediate  predeces- 
sors, and  the  decadence  of  the  art  in  the 
ensuing  period  may  be  traced  not  alone  to  the  false 


"iRJANqUlHAR/JYNOnrw  ctthe 
lAfT  JUDQMHNT,!!  CiAR.TQLDMMBD 


THE.   EMPLOYME-NT  OF  THE   EQUILATBRAU^ 
TItlANGLL  IN  R.ENAI5SANCL  PAINTINO-n. 


THRCANGIANI  HOLY-- 
--FAMILY  BY  RAPHAE-U 


^nczz 


^R 


^fi^- 


ANNUNCIATION,  FRA  EAJCTOLOMMEO 


THE  LAST-yuPPtR.,  CE-NTER.  THEi  AAADONNA  DEL.  -SACCO.  BY 
ONLY.  (R£ST0R£D)  BV  CA  VINCI  ANDR£A  Dbb  SARSTO 


55 


54 

sentiment  and  affectation 
of  the  times,  but  also 
in  the  abandonment  by 
the  artists  of  those 
obscurely  geometrical 
arrangements  and  group- 
ings which,  in  the  works 
of  the  greatest  masters, 
so  satisfy  the  eye  and 
haunt  the  memory  of 
the  beholder  (Illustra- 
tions 55,  56). 

Sculpture,  even  more 
than  painting,  is  based 
on  geometry.  The  colos- 
si of  Egypt,  the  bas- 
reliefs  of  Assyria,  the 
figured  pediments  and 
metopes  of  the  temples 
of  Greece,  the  carved 
tombs  of  Ravenna,  the 
Delia  Robbia  lunettes, 
the  sculptured  tympani 
of  Gothic  church  portals. 


LATENT  GEOMETRY 


63 


GEOMETRICAL  bASlS  OF  THE  S15TINE  CEILING  PAINTINQJ 


56 


all  alike  lend  themselves  in  greater  or  less  degree 
to  a  geometrical  synopsis  (Illustration  57). 
Whenever  sculpture  suffered  divorce  from 
architecture,  the  geometrical  element  became 
less  prominent,  doubtless  because  of  all  the  arts 
architecture  is  the  most  clearly  and  closely 
related  to  geometry.  Indeed,  it  may  be  said  that 
architecture  is  geometry  made  visible,  in  the 
same  sense  that  music  is  number  made  audible. 
A  building  is  an  aggregation  of  the  commonest 
geometrical  forms :  parallelograms,  prisms,  pyr- 
amids, and  cones, — the  cylinder  appearing  in 
the  column,  and  the  hemisphere  in  the  dome. 
The  plans,  likewise,  of  the  world's  famous  build- 
ings, reduced  to  their  simplest  expression,  are  discovered  to  resolve  them- 
selves into  a  few  simple  geometrical  figures  (Illustration  58). 

But  architecture  is  geometrical  in  another  and  a  higher  sense  than  this. 
Emerson  says:  "The  pleasure  a  palace  or  a  temple  gives  the  eye  is  that  an 
order  and  a  method  has  been  communicated  to  stones,  so  that  they  speak  and 
geometrize,  become  tender  or  sublime  with  expression."  All  truly  great 
and  beautiful  works  of  architecture — from  the  Egyptian  pyramids  to  the 


64 


THE  BEAUTIFUL  NECESSITY 


cathedrals  of  the  Ile-de-France — are  harmoniously  proportioned,  their  prin- 
cipal and  subsidiary  masses  being  related,  sometimes  obviously,  more  often 
obscurely,  to  certain  symmetrical  figures  of  geometry,  which,  though  invisible 
to  the  sight,  and  not  consciously  present  in  the  mind  of  the  beholder,  yet 
perform  the  important  function  of  co-ordinating  the  entire  fabric  into  one 
easily  remembered  whole.  Upon  some  such  principle  is  surely  founded  what 
Symonds  calls  "that  severe  and  lofty  art  of  composition  which  seeks  the 
highest  beauty  of  design  in  architectural  harmony  supreme,  above  the 
melodies  of  gracefulness  of  detail." 

There  is  abundant  evidence  in  support  of  the  theory  that  the  builders 
of  antiquity,  the  masonic  guilds  of  the  Middle  Ages,  and  the  architects  of  the 
Italian  Renaissance,  knew  and  followed  certain  rules ;  but  though  this  theory 
be  denied,  or  even  disproven,  if  after  all  these  men  obtained  their  results 


"THE  Q0OMETRICAL  bASlS  C^  THE  PLAN  IN  MCHIT^TURAL  DESIGN 


T5RAMANTE3IUN 
K3R.  ST.  PETSSiS 


TfiMPLE  C*  ZEIUS 
AT  A&EIQfiNTtM 


TTPAUIiS 
lONDON, 


THE  DUOMO 
ATHOiNGE 


THE  BWrreCN        TH  CHlMOi  C* 
AT  RONE  5  SIMEC^T  STYIXES 


r-\ 


KICHELAIJQELD'^ 
PLANFCiLi  PETERS 


^ 


PIAN  FOR-  S  BVUlIS 


THECEKTOJA 
AT  PAVIA 


NOTRE  n»Mi 
Af  PARIS 


HOIXAND 
HOU^ 


58 


CATHEDRAL 
AT  £CeJ?AH 


SAU^tTEY 
CATHEDRAL 


G 


INIQOJDNE^'niAN 

Kst^A/HIT£J^A^^ 


£i£NHElM 


LATENT  GEOMETRY 


6S 


PAUADLAN  VIIXA  NElAJL-  VICENZA 


unconsciously,  their  creations  so 
lend  themselves  to  a  geometrical 
analysis  that  the  claim  for  the  ex- 
istence of  certain  canons  of  propor- 
tion, based  on  geometry,  remains 
unimpeached. 

The  plane  figures  principally  em- 
ployed in  determining  architectural 
proportion  are  the  circle,  the  equi- 
lateral triangle,  and  the  square — 
which  also  yields  the  right  angled 
isosceles  triangle.  It  will  be  noted 
that  these  are  the  two-dimensional 
correlatives  of  the. sphere,  the  tetra- 
hedron, and  the  cube,  mentioned  as 
being  among  the  determining  forms 
in  molecular  structure.  The  question 
naturally  arises,  why  the  circle,  the 
equilateral  triangle  and  the  square? 
Because,  aside  from  the  fact  that 
they  are  of  all  plane  figures  the  most 
elementary,  they  are  intimately  re- 
lated to  the  body  of  man,  as  has  been 
shown  (Illustration  45),  and  the 
body  of  man  is,  as  it  were,  the  architectural  archetype.  But  this  simply 
removes  the  inquiry  to  a  different  field,  it  does  not  answer  it.  Why  is  the 
body  of  man  so  constructed  and  related?  This  leads  us,  as  does  every 
question,  to  the  threshold  of  a  mystery  upon  which  theosophy  alone  is  able 
to  throw  light.  Any  extended  elucidation  would  be  out  of  place  here:  it 
is  sufficient  to  remind  the  reader  that  the  circle  is  the  symbol  of  the  universe, 
the  equilateral  triangle  of  the  higher  trinity  {atma,  buddhi,  manas),  and  the 
square  of  the  lower  quatrinary,  of  man's  sevenfold  nature. 

The  square  is  principally  used  in  preliminary  plotting :  it  is  the  determin- 
ing figure  in  many  of  the  palaces  of  the  Italian  Renaissance ;  the  Arc  d'Etoille 
in  Paris  is  a  modern  example  of  its  use  (Illustrations  59,  60).  The  circle  is 
most  often  employed  in  conjunction  with  the  square  and  the  triangle.  In 
Thomas  Jefferson's  Rotunda  for  the  University  of  Virginia,  a  single  great 


ARjC  DE  Tii^IOMPHE:  WT  PAR^IX 


59 


66 


THE  BEAUTIFUL  NECESSITY 


£QYPTIAN 


QlteEI<^ 


RjOMAN 


MEDIAEVAL 


60 

point  of  geometry,  is  the  equilateral  triangle, 
has  an  especial  fondness  for  this  figure,  just 
related  sounds.  Indeed,  it  might  not  be  too 
fanciful  to  assert  that  the  common  chord  of 
any  key  (the  tonic  with  its  third  and  fifth)  is 
the  musical  equivalent  of  the  equilateral  tri- 
angle. It  is  scarcely  necessary  to  dwell  upon 
the  properties  and  unique  perfection  of  this 
figure.  Of  all  regular  polygons  it  is  the 
simplest;  its  three  equal  sides  subtend  equal 
angles,  each  of  60  degrees;  it  trisects  the 
circumference  of  a  circle;  it  is  the  graphic 
symbol  of  the  number  three,  and  hence 
of    every    three-fold    thing;    doubled,    its 


circle  was  the  determin- 
ing figure,  as  his  original 
pen  sketch  of  the  build- 
ing shows.  Some  of  the 
best  Roman  triumphal 
arches  submit  themselves 
to  a  circular  synopsis, 
and  a  system  of  double 
intersecting  circles  has 
been  applied,  with  inter- 
esting results,  to  fagades 
as  widely  different  as 
those  of  the  Parthenon 
and  the  Farnese  Palace 
in  Rome,  though  it  would 
be  fatuous  to  claim  that 
these  figures  determined 
the  proportions  of  these 
fagades. 

By  far  the  most  im- 
portant figure  in  archi- 
tectural proportion,  con- 
sidered from  the  stand- 
It  would  seem  that  the  eye 
as  the  ear  has,  for  certain 


lOR^THE  ROTUNDA  OP  THE 
UNIveiLflTY  OF  VlRidlNIA 


LATENT  GEOMETRY 


(fj 


APPLICATION  OF  THE  EQUILATERAL 
TRJANGLE  TO  THE  ER.ECHTHEUM-— 

AT  ATHENS 


WE^T  5IDL 


PORJCH  OF  THE/ CARYATIDES 


62 


68 


THE  BEAUTIFUL  NECESSITY 


generating  arcs  form  the  vesica  piscis,  of  so  frequent  occurrence  in  early 
Christian  art;  two  symmetrically  intersecting  equilateral  triangles  yield  the 
figure  known  as  "Solomon's  Seal,"  or  the  "Shield  of  David,"  to  which  mystic 
properties  have  always  been  ascribed. 


63 

It  may  be  stated  as  a  general  rule 
that  whenever  three  important  points 
in  any  architectural  composition  coin- 
cide (approximately  or  exactly)  with 
the  three  extremities  of  an  equilateral 
triangle,  it  makes  for  beauty  of  propor- 
tion. An  ancient  and  notable  example 
occurs  in  the  pyramids  of  Egypt,  the 
sides  of  which,  in  their  original  con- 
dition, are  believed  to  have  been  equi- 
lateral triangles.  It  is  a  demonstrable 
fact  that  certain  geometrical  intersec- 
tions yield  the  important  proportions 
of  Greek  architecture.  The  perfect 
little  Erechtheum  would  seem  to  have 
been  proportioned  by  means  of  the 
equilateral  triangle  and  the  angle  of 
60  degrees,  both  in  general  and  in 
detail  (Illustration  62).  The  same 
angle,  erected  from  the  central  axis  of 
a  column  at  the  point  where  it  inter- 
sects the  architrave,  determines  both 
the  projection  of  the  cornice  and  the 


THE'  BQUILATE-RALTRMNGLL  IN 
RjCiMAN  ARCHITECTURE 


ARCH  OF  TITUS.  ROfAt 


A  SECTION  OF  THE^  PANTHEON,  RX3fAI> 


64 


LATENT  GEOMETRY 


69 


THE  E/IJUILATBRAL  TRIANGLE-  IN  ITALIAN  ARCHITBCTUIIE. 

(ltENAI5^:ANCE) 


WINEOW  IN  A  ROMAN  PALACE     SECTION  OF  BASILICA  OF  SAN  LORX-NZO.  FLOR£.NCR 


65 


height  of  the  architrave,  in  many  of  the  finest  Greek  and  Roman  temples 
(Illustrations  67-70).  The  equilateral  triangle  used  in  conjunction  with  the 
circle  and  the  square  was  employed  by  the  Romans  in  determining  the 
proportions  of  triumphal  arches,  basilicas  and  baths.  That  the  same  figure 
was  a  factor  in  the  designing  of  Gothic  cathedrals  is  sufficiently  indicated 
in  the  accompanying  facsimile  reproduction  of  an  illustration  from  the  Como 
Vitruvius,  published  in  Milan  in  1521,  which  shows  a  vertical  section  of  the 
Milan  cathedral  and  the  system  of  equilateral  triangles  which  determined 
its  various  parts  (Illustration  71).  The  vesica  piscis  was  often  used  to 
establish  the  two  main  internal  dimensions  of  the  cathedral  plan ;  the  greatest 
diameter  of  the  figure  corresponding  with  the  width  across  the  transepts,  the 
upper  apex  marking  the  limit  of  the  apse,  and  the  lower,  the  termination  of 
the  nave.  Such  a  proportion  is  seen  to  be  both  subtle  and  simple,  and 
possesses  the  advantage  of  being  easily  laid  out.  The  architects  of  the 
Italian  Renaissance  doubtless  inherited  certain  of  the  Roman  canons  of 
architectural  proportion,  for  they  seem  very  generally  to  have  recognized 
them  as  an  essential  principle  of  design. 

Nevertheless,  when  all  is  said,  it  is  easy  to  exaggerate  the  importance  of 
this  matter  of  geometrical  proportion.  The  designer  who  seeks  the  ultimate 
secret  of  architectural  harmony  in  mathematics  rather  than  in  the  trained 


70 


THE  BEAUTIFUL  NECESSITY 


eye,  is  following  the  wrong  road  to  success.  A  happy  inspiration  is  worth  all 
the  formulas  in  the  world — if  it  is  really  happy,  the  artist  will  probably  find 
that  he  has  "followed  the  rules  without  knowing  them."  Even  while  formu- 
lating concepts  of  art  the  author  must  again  reiterate  that  the  concept  is 
unfruitful  in  art.  The  "mechanism"  of  spatial  beauty  is  an  interesting  study, 
and  within  certain  limits,  a  useful  one;  but  it  can  never  take  the  place  of 
the  creative  faculty,  it  can  only  restrain  and  direct  it.  The  study  of  propor- 
tion is  to  the  architect  what  the  study  of  harmony  is  to  a  musician, — it  helps 
his  genius  adequately  to  express  itself. 


THE.  HEXAGRAM  IN  GOTHIC  ARCHITECTUR£ 

SEXrriON  OF  WINDOW  MUbUONS  IN  THE/ 

aSEfiSTORY.  WINGHBSTBItCATHDDRAL. 

(FROWVOWIL/T) 


RDSBWINDOW  IN  SOUTH  TRANSEPT 
OPRDUE-N  CATHE.DRAL  (FROM.  GWIO) 


66 


LATENT  GEOMETRY 


71 


67 


72 


THE  BEAUTIFUL  NECESSITY 


LATENT  GEOMETRY 


73 


■^■l.--L'X'-f-fl'fl'l'l'^'-l'^'i.'j'l.'^'^'l'.»'jl'i'l'l'l'l'l'l'l'kjll 


69 


74 


THE  BEAUTIFUL  NECESSITY 


70 


LATENT  GEOAIETRY 


75 


LIBER, 


PRIMVS 


Idea  giometricae  archttectonicae  ab  ichnogiiaphia  svmpta.-vtpebamvssinza.s  possnrr 

PER  ORXHOGRAPHIAM  AC  SCAENOQKAPH.'AJ/!  PERDVCERE  OMNES  Q.ASCVNQyAE  UNEAS^NOKt 
SOLVM  AD    CLRCINl   CENTRVM<  SED   Q.\ft£  ATIUGONO  ET  Q\AD!lATO   AVT  ALIO  QVOVISMODO 
PZaVENIVNTPOSSINTSWM  HABERE  EESPONSVM  <  TVM  FEB-  EVRYTHMIAM   PROPOR^ 
TIONATAM   QVANTVM  ETIAM*  SYMMETRIAE  QVAKTITATEM    OKDINARIAM  AC  PER. 
OPERJS'.DECORATIONEM   OSTENDrRE-.VTI  ETIAM  HEC  O  VA£  A  GERMANICO  MOREPEKVE' 
KTVNT  CI  ST  RIB VINTVR.PENZ  QVEMADMODVH    SACRA    CATHEDKALIS  AESES  MEOlOLAtU 
PAT£TaEX«*-*  PAMfcC*  C*A.*PaVX-  QJ-C<  AC   AP4D  ». 


VI 
THE  ARITHMETIC  OF  BEAUTY 

ALTHOUGH  architecture  is  based  primarily  upon  geometry,  it  is  pos- 
sible to  express  all  spatial  relations  numerically,  for  arithmetic,  and 
not  geometry,  is  the  universal  science  of  quantity.  The  relation  of 
masses  one  to  another — of  voids  to  solids,  and  of  heights  and  lengths  to 
widths — form  ratios;  and  when  such  ratios  are  simple  and  harmonious, 
architecture  may  be  said,  in  Walter  Pater's  famous  phrase,  to  "aspire 
towards  the  condition  of  music."  The  trained  eye,  and  not  an  arithmetical 
formvila,  determines  what  is,  and  what  is  not,  beautiful  proportion.  Never- 
theless the  fact  that  the  eye  instinctively  rejects  certain  proportions  as  un- 
pleasing,  and  accepts  others  as  satisfactory,  is  an  indication  of  the  existence 
of  spatial  laws  based  upon  number,  not  unlike  those  which  govern  musical 
harmony.  The  secret  of  the  deep  reasonableness  of  such  selection  by  the 
senses  lies  hidden  in  the  very  nature  of  number  itself,  for  number  is  the 
invisible  thread  on  which  the  worlds  are  strung — the  universe  abstractly 
symbolized. 

Number  is  the  within  of  all  things, — the  "first  form  of  Brahman."  It 
is  the  measure  of  time  and  space ;  it  lurks  in  the  heart  beat  and  is  blazoned 
upon  the  starred  canopy  of  night.  Substance,  in  a  state  of  vibration,  that 
is,  conditioned  by  number,  ceaselessly  undergoes  the  myriad  transmutations 
which  produce  phenomenal  life.  Elements  separate  and  combine  chemically 
according  to  numerical  ratios:  "Moon,  plant,  gas,  crystal  are  concrete 
geometry  and  number."  By  the  Pythagoreans  and  by  the  ancient  Egyptians 
sex  was  attributed  to  numbers,  odd  numbers  being  conceived  of  as  masculine, 
or  generating,  and  even  numbers  as  feminine,  or  parturitive,  on  account  of 

[76] 


VI 


THE  ARITHMETIC  OF  BEAUTY 


n 


2=99 

3=1 
4=( 


Il 


4   ^  J^ 

MASC.f  FE^M.]NEUT 
SEIUE-SlSEKIESlSEIUBS 


their  infinite  divisibility.  Harmonious 
combinations  were  those  involving  the 
marriage  of  a  masculine  and  a  femin- 
ine— an  odd  and  an  even — number. 

Number  proceeds  from  unity  towards 
infinity,  and  returns  again  to  unity  as 
the  soul,  defined  by  Pythagoras  as  a 
self-moving  number,  goes  forth  from, 
and  returns  to  Cod.  These  two  acts, 
one  of  projection,  and  the  other  of 
recall;  these  two  forces,  centrifugal 
and  centripetal,  are  symbolized  in  the 
operations  of  addition  and  subtraction. 
Within  them  is  embraced  the  whole  of 
computation;  but  because  every  num- 
ber, every  aggregation  of  units,  is  also 
a  new  unit  capable  of  being  added 
or  subtracted,  there  are  also  the  opera- 
tions of  multiplication  and  division, 
which  consist,  in  the  one  case,  of  the 
addition  of  several  equal  numbers 
together,  and  in  the  other,  of  the 
subtraction  of  several  equal  numbers  from  a  greater  until  that  is  exhausted. 
The  progression  and  retrogression  of  numbers  in  groups  expressed  by 
the  multiplication  table  gives  rise  to  what  may  be  termed  "numerical  con- 
junctions."   These  are  analogous  to  astronomical  conjunctions :   the  planets, 

revolving  around  the  sun  at  dif- 
ferent rates  of  speed,  and  in  wide- 
ly separated  orbits,  at  certain  times 
come  into  line  with  each  other 
and  with  the  sun.  They  are  then 
said  to  be  in  conjunction.  Simi- 
larly, numbers,  advancing  towards 
infinity  singly  and  in  groups 
(expressed  by  the  multiplication 
table),  at  certain  stages  of  their  progression  come  into  relation  with  one 
another.     For  example,  an  important  conjunction  occurs  in  12,  for  of  a 


49.  0?o. 
71AKBN 
7TIME$ 


•A  GRAPHIC  r/JTEM  OF  NOTATION. 


72 


78 


THE  BEAUTIFUL  NECESSITY 


VI 


THE/  NUME.RICAL  BASIS  O^THB 
ARjCHITIECTURAL    t 


series  of  twos  it  is  the  sixth,  of  threes 
the  fourth,  of  fours  the  third,  and  of 
sixes  the  second.  It  stands  to  8  in 
the  ratio  of  3 :2,  and  to  9  of  4 :3. 
It  is  related  to  7  through  being  the 
product  of  3  and  4,  of  which  numbers 
7  is  the  sum.  Eleven  and  thirteen 
are  not  conjunctive  numbers.  Four- 
teen is  so  in  the  series  of  twos,  fours, 
and  sevens;  15  is  so  in  the  series  of 
fives  and  threes.  The  next  conjunc- 
tion after  12,  of  3  and  4  and  their 
first  multiples,  is  in  24,  and  the  next 
following  is  36,  which  numbers  are 
respectively  the  two  and  three  of  a 
series  of  twelves,  each  end  being  but 
a  new  beginning. 

It  will  be  seen  that  this  discovery 
of  numerical  conjunctions  consists 
merely  of  resolving  numbers  into  their 
prime  factors,  and  that  a  conjunctive 
number  is  a  common  multiple ;  but  by 
naming  it  so,  to  dismiss  the  entire 
subject  as  known  and  exhausted,  is  to  miss  a  sense  of  the  wonder,  beauty, 
and  rhythm  of  it  all,  a  mental  impression  analogous  to  that  made  upon  the 


THE/  TUSCAN.  D03RiO,  AND  IONIC  OEDLILS 
ACXORDINQ  TD  VIGNOLE.— ^PitOPORTIONX 
DETTERMINED  5Y  THE-  ^fUMBEE,J  3,  4,  AND 
THBiR>  CONJUNCTIVE-  NUMBER^,  12- • 


74 


THE-  Rf^LATION  &ETWE>E.N  THE. 
SUBMINOR.  SEA/E.NTH  (4  ".7)  AND 
THE,  RQUILATSRAL  TItlANGL&'N' 

75 


VI 


THE  ARITHMETIC  OF  BEAUTY 


79 


eye  by  the  swift  glancing  balls  of  a  juggler, 
the  evolutions  of  drilling  troops,  or  the 
intricate  figures  of  a  dance,  for  these  things 
are  number  concrete  and  animate  in  time 
and  space. 

The  truths  of  number  are  of  all  truths 
the  most  interior,  abstract,  and  difficult  of 
apprehension,  and  since  knowledge  becomes 
clear  and  definite  to  the  extent  that  it  can 
be  made  to  enter  the  mind  through  the 
channels  of  physical  sense,  it  is  well  to 
accustom  oneself  to  conceiving  of  number 
graphically,  by  means  of  geometrical  sym- 
bols (Illustration  ^2),  rather  than  in  terms 
of  the  familiar  Arabic  notation  which, 
though  admirable  for  purposes  of  com- 
putation, is  of  too  condensed  and  arbitrary 


THE.  BANQUEriNG  HOU^.\A«rrEHAU/ 


OLD  JONffiXJEXHSUJL. 


i  (i 
i 


77 

a  character  to  reveal  the 
properties  of  individual 
numbers.  To  state,  for 
example,  that  4  is  the  first 
square,  and  8  the  first  cube, 
conveys  but  a  vague  idea  to 
most  persons,  but  if  4  be 
represented  as  a  square  en- 
closing four  smaller  squares, 
and  8  as  a  cube  containing 
eight  smaller  cubes,  the  idea 
is  apprehended  immediately 
and  without  effort.  Three  is, 
of  course,  the  triangle;  the 
irregular  and  vital  beauty  of 
the  number  5  appears  clearly 
in  the  heptalpha,  or  five- 
pointed  star ;  the  faultless  symmetry  of  6,  its  relation  to  3  and  2,  and  its  regu- 
lar division  of  the  circle,  are  portrayed  in  the  familiar  hexagram  known  as  the 


£Pr5COPAD PALACE  AT  I-EON",  7AS  v3 AND4 

-r^"""Tiiiiiri"r""T"""' 


PALACE.  IN  V1CEN2AT  PALACE-  IN  ROME^ 
7 AS  2.2.AND3       1        8AS  JANOy^ 


78 


8o 


THE  BEAUTIFUL  NECESSITY 


VI 


THE»  aSjOUSrtA  AT  MANTUA,  j  VfsLKOO  UGUCCIONl  AT  FLCRfNCR 


V>ALKVZO  EAE3TOUN1.  FLORtNCt     2MJiZZO  TftCCONI,  BOLOGNA. 

\5^RIOU;  miACR  FAQAD&5~  3  WED  AS  A  MUDTIPLE. 


79 

the  nature  of  color;  music,  of  sound  in  wood, 
strings ;  architecture  shows  forth  the  quaHties  of 
beauty  of  materials.  All  of  the  arts, 
and  particularly  music  and  architec- 
ture, portray  in  different  manners  and 
degrees  the  truths  of  number.  Archi- 
tecture does  this  in  two  ways :  esoteri- 
cally,  as  it  were,  in  the  form  of  har- 
monic proportions;  and  exoterically 
in  the  form  of  symbols  which  repre- 
sent numbers  and  groups  of  numbers. 
The  fact  that  a  series  of  threes  and  a 
series  of  fours  mutually  conjoin  in  12, 


Shield  of  David.  Seven, 
when  represented  as  a 
compact  group  of  circles, 
reveals  itself  as  a  number 
of  singular  beauty  and 
perfection  worthy  of  the 
important  place  accorded 
to  it  in  all  mystical  phi- 
losophy. It  is  a  curious 
fact  that  when  asked  to 
think  of  any  number  less 
than  10,  most  persons 
will  choose  7  (Illustra- 
tion 73). 

Every  form  of  art, 
though  primarily  a  vehi- 
cle for  the  expression 
and  transmission  of  par- 
ticular ideas  and  emo- 
tions, has  subsidiary  of- 
fices, just  as  a  musical 
tone  has  harmonics 
which  render  it  more 
sweet.  Painting  reveals 
in  brass,  and  in  stretched 
light,  and  the  strength  and 


VI 


THE  ARITHMETIC  OF  BEAUTY 


8i 


finds  an  architectural  ex- 
pression in  the  Tuscan,  the 
Doric,  and  the  Ionic  orders 
according  to  Vignole,  for 
in  them  all  the  stylobate  is 
four  parts,  the  entablature 
3,  and  the  intermediate 
column  12  (Illustration 
74).  The  affinity  between 
4  and  7,  revealed  in  the 
fact  that  they  express  the 
ratio  between  the  base  and 
the  altitude  of  the  right- 
angled  triangle  which  forms 
half  of  an  equilateral,  and 
the  musical  intervals  of  the 
diminished  seventh  (Illustration  75)  is  architecturally  suggested  in  the 
Palazzo  Giraud,  which  is  four  stories  in  height  with  seven  openings  in  each 
story  (Illustration  76). 
Every  building  is  a 
symbol  of  some  number 
or  group  of  numbers, 
and  other  things  being 
equal  the  more  perfect 
the  numbers  involved  the 
more  beautiful  will  be 
the  building  (Illustra- 
tions 77-83).  Three,  5, 
and  7 — the  numbers 
which  occur  oftenest — 
are  the  most  satisfactory 
because,  being  of  small 
quantity,  they  are  easily  grasped  by  the  eye,  and  being  odd,  they  yield  a  center 
or  axis,  so  necessary  in  every  architectural  composition.  Next  in  value  are 
the  lowest  multiples  of  these  numbers  and  the  least  common  multiples  of  any 
two  of  them,  because  the  eye,  with  a  little  assistance,  is  able  to  resolve  them 
into  their  constituent  factors.    It  is  part  of  the  art  of  architecture  to  render 


82 


THE  BEAUTIFUL  NECESSITY 


VI 


Hi  -Bi  'fl(  'js  Bf  'S  'S      iiii 


ill    lllfiil    II 


pi 


OOUJEQ&  CPTHE/5APIE/N2A.  ATECME/' -AN 

lUAWTEiKriON  OFTHE/VAl-UE/OFAVEJSjriCAL 
AND  H0EI20NTAb  DIVISION  OF  A  FAi;:ADB  TOAS- 
JUT  THE  BYE.  TO  AN  APPREHENi'ION'  (^  THE^ 
NUMBE-B  0£i  NUMBERS  OF  WHICH  IT  15  THE^ 
EXPRBJJrON.  IN  THI^  CASE  21  .THE  PRCDUOT 
OF0AND7. 


83 


such  assistance,  for  the  eye  counts 
always,  consciously  or  unconsciously, 
and  when  it  is  confronted  with  a 
number  of  units  greater  than  it  can 
readily  resolve,  it  is  refreshed  and 
rested  if  these  units  are  so  grouped 
and  arranged  that  they  reveal  them- 
selves as  factors  of  some  higher 
quantity. 

There  is  a  raison  d'etre  for  string 
courses  other  than  to  mark  the  posi- 
tion of  a  floor  on  the  interior  of  a 
building,  and  for  quoins  and  pilasters 
other  than  to  indicate  the  presence 
of  a  transverse  wall.  These  some- 
times serve  the  useful  purpose  of  so 
subdividing  a  fagade  that  the  eye 
estimates  the  number  of  its  openings 
without  conscious  effort  and  consequent  fatigue  (Illustration  83).  The 
tracery  of  Gothic  rose-windows  forms  perhaps  the  highest  and  finest  archi- 
tectural expression  of  number  (Illustration  84).    Just  as  thirst  makes  water 

more  sweet,  so  does 
Gothic  tracery  confuse 
the  eye  with  its  com- 
plexity only  the  more 
greatly  to  gratify  the 
sight  by  revealing  the 
inherent  simplicity  in 
which  this  complexity 
has  its  root.  Some- 
times, as  in  the  case 
of  the  Venetian  Ducal 
Palace,  the  numbers  in- 
volved are  too  great 
for  counting,  but  other 
and  different  arithmetical  truths  are  portrayed ;  for  example,  the  multiplica- 
tion of  the  first  arcade  by  2  in  the  second,  and  this  by  3  in  the  cusped  arches, 


BEAUVSMJ  OOKCRAI/  |^.  OUEN.KWEN. 


BASED  CN  THE.  HEX 
AGIiAM.  OK.  NUMBER, 


BASED  ON  THE 
PE.NTALFHA,5 


CWra  MUDnPL£5a.4.  lMUmPLEOF3 

ROSE.  WINDOW  IN  WE5T 
TEANiEPT  OF  Tit  CHURCH 
OF  STOtJEN.RDUEN:  BASED 
ON  THE  QEAPHIC  SYMEa 
FOR;  THE  NUMBER  SEVEN 

ANUMLRICAL  ANALYSIS  OF  GOTHIC  TRACLIbY 


84 


VI 


THE  ARITHMETIC  OF  BEAUTY 


83 


NUMEJ2AIKK  ttT  QECUPJ' EXPR£^ra3  AECHntCTTJEAUy 


ii.   M.   M    M    ii    ii    M. 


A  BUND  AECADB  IN  THE- SOUTH 
TRANJEPT  OP  THE  CHAPEL  OF- 
UNCOLN  CATHEDEAl^ 


and   by   4   in   the   quatrefoils    im- 
mediately above. 

Seven  is  proverbially  the  perfect 
number.  It  is  of  a  quantity  suf- 
ficiently complex  to  stimulate  the 
eye  to  resolve  it,  and  yet  so  simple 
that  it  can  be  to  analyzed  at  a 
glance;  as  a  center  with  two  equal 
sides,  it  is  possessed  of  symmetry, 
and  as  the  sum  of  an  odd  and  even 
number  (3  and  4),  it  has  vitality 
and  variety.  All  these  properties  a 
work  of  architecture  can  variously 
reveal  (Illustration  78).  Fifteen, 
also,  is  a  number  of  great  perfec- 
tion. It  is  possible  to  arrange  the  first  9  numbers  in  the  form  of  a  "magic" 
square  so  that  the  sum  of  each  line,  read  across  or  up  or  down,  will  be  15. 

Thus: 


PALAZZO  VnKTEi^Sl 
QIMIGNANO 


JAN 


R£NAi;iANCE. 

ORNAMENT 


85 


AItCHITEX:TURAb  OR^NAMUTT 
OOW1DER£D  AS  TI^ 
OBJECTIFlGftOriON 
OFNUMELR__. 


TVATO 


MUUnPLICATION 
INGItOURTOFFIVL 


THR££ 


ALT&RNATION  CP 
THE£E  AND  SU>/Eti 


4 

9 

2-15 

3 

5 

7-15 

8 

I 

6    =     15 

86 


15  15  15 

Its  beauty  is  portrayed  geometrically  in  the 
accompanying  figure  which  expresses  it, 
being  15  triangles  in  three  groups  of  5 
(Illustration  87).  Few  arrangements  of 
openings  in  a  fagade  better  satisfy  the  eye 
than  three  superim- 
posed groups  of  five 
(Illustrations  yy, 
81).    May  not  one 


source   of   this   satisfaction   dwell   in  the   intrinsic 
beauty  of  the  number  15? 

In  conclusion,  it  is  perhaps  well  that  the  reader 
be  again  reminded  that  these  are  the  by-ways,  and 
not  the  highways  of  architecture :  that  the  highest 


84  THE  BEAUTIFUL  NECESSITY  vi 

beauty  comes  always,  not  from  beautiful  numbers,  nor  from  likenesses  to 
Nature's  eternal  patterns  of  the  world,  but  from  utility,  fitness,  economy, 
and  the  perfect  adaptation  of  means  to  ends.  But  along  with  this  truth 
there  goes  another :  that  in  every  excellent  work  of  architecture,  in  addition 
to  its  obvious  and  individual  beauty,  there  dwells  an  esoteric  and  universal 
beauty,  following  as  it  does,  the  archetypal  pattern  laid  down  by  the  Great 
Architect  for  the  building  of  that  temple  which  is  the  world  wherein  we  dwell. 


VII 
FROZEN  MUSIC 

IN  the  series  of  essays  of  which  this  is  the  final  one,  the  author  has 
undertaken  to  enforce  the  truth  that  evolution  on  any  plane  and  on  any 
scale  proceeds  according  to  certain  laws  which  are  in  reality  only 
ramifications  of  one  ubiquitous  and  ever  operative  law;  that  this  law 
registers  itself  in  the  thing  evolved,  leaving  stamped  thereon,  as  it  were, 
fossil  footprints  by  means  of  which  it  may  be  known.  In  the  arts  the 
creative  spirit  of  man  is  at  its  freest  and  finest  and  nowhere  among  the  arts 
is  it  so  free  and  so  fine  as  in  music.  In  music,  accordingly,  the  universal  law 
of  becoming  finds  instant,  direct,  and  perfect  self-expression;  music  voices 
the  inner  nature  of  the  will-to-live  in  all  its  moods  and  moments ;  in  it,  form, 
content,  means  and  end,  are  perfectly  fused.  It  is  this  fact  which  gives 
validity  to  the  before  quoted  saying  that  all  of  the  arts  "aspire  towards  the 
condition  of  music."  All  aspire  to  express  the  law,  but  music,  being  unin- 
cumbered by  the  leaden  burden  of  gross  physical  matter,  expresses  it  most 
easily  and  adequately.  This  being  so,  there  is  nothing  unreasonable  in  at- 
tempting to  apply  the  known  facts  of  musical  harmony  and  rhythm  to  any 
other  art,  and  since  these  essays  concern  themselves  primarily  with  archi- 
tecture, the  final  aspect  in  which  that  art  will  be  presented  here  is  as  "frozen 
music" — ponderable  matter  governed  by  musical  law. 

Music  depends  primarily  upon  the  equal  and  regular  division  of  time 
into  beats,  and  of  these  beats  into  measures.  Over  this  soundless  and 
invisible  warp  is  woven  an  infinitely  various  melodic  pattern,  made  up  of 
tones  of  different  pitch  and  duration  arithmetically  related  and  combined, 
according  to  the  laws  of  harmony.     Architecture,  correspondingly,  implies 

[8s] 


86 


THE  BEAUTIFUL  NECESSITY 


VII 


THE.  NORJVIAN  PORCH  CANTE,R>- 
BURJ<'~AN  ARCHITECTURAL  Ei(-- 
PR^SSICSN  OP  A  NOTE  &t.  HARMONICS 


the  rhythmical  division  of  space,  and  obedience  to  laws  numerical  and 
geometrical.  A  certain  identity,  therefore,  exists  between  simple  harmony 
in  music,  and  simple  proportion  in  architecture.  By  translating  the  con- 
sonant tone  intervals  into  number,  the  common  denominator,  as  it  were,  of 
both  arts,  it  is  possible  to  give  these  intervals  a  spatial,  and  hence  an  archi- 
tectural expression.  Such  expression,  considered  as  proportion  only  and 
divorced  from  ornament,  will  prove  pleasing  to  the  eye  in  the  same  way 

that  its  correlative  is  pleasing  to  the  ear, 
because  in  either  case  it  is  not  alone  the 
special  organ  of  sense  which  is  gratified, 
but  that  inner  Self,  in  which  all  senses  are 
one.  Containing  within  Itself  the  mystery 
of  number,  It  thrills  responsive  to  every 
audible  or  visible  presentment  of  that 
mystery. 

If  a  vibrating  string  yielding  a  certain 
musical  note  be  stopped  in  its  center,  that 
is,  divided  by  half,  it  will  then  sound  the 
octave  of  that  note.  The  numerical  ratio 
which  expresses  the  interval  of  the  octave 
is  therefore  i  :2.  If  one-third  instead  of 
one-half  of  the  string  be  stopped,  and  the 
remaining  two-thirds  struck,  it  will  yield 
the  musical  fifth  of  the  original  note,  which 
thus  corresponds  to  the  ratio  2 :3.  The  length  represented  by  3  4  yields  the 
fourth ;  4 :5  the  major  third ;  and  5  :6  the  minor  third.  These  comprise  the 
principal  consonant  intervals  within  the  scope  of  one  octave.  The  ratios  of 
inverted  intervals,  so  called,  are  found  by  doubling  the  smaller  number  of 
the  original  interval  as  given  above.  2  :^,  the  fifth,  gives  3  14,  the  fourth ; 
4:5,  the  major  third,  gives  5:8,  the  minor  sixth;  5:6,  the  minor  third,  gives 
6:10,  or  3:5,  the  major  sixth. 

Of  these  various  consonant  intervals  the  octave,  fifth,  and  major  third 
are  the  most  important,  in  the  sense  of  being  the  most  perfect,  and  they  are 
expressed  by  numbers  of  the  smallest  quantity,  an  odd  number  and  an  even. 
It  will  be  noted  that  all  of  the  intervals  above  given  are  expressed  by  the 
numbers  i,  2,  3,  4,  5  and  6,  except  the  minor  sixth  (5:8),  and  this  is  the 
most  imperfect  of  all  consonant  intervals.    The  sub-minor  seventh,  expressed 


VII 


FROZEN  MUSIC 


87 


ARCH1TECTUR.E/  AS  HARMONY  Tno  scm*) 

VAItlOUJ  RENA]XXAN0E/\A/INDOV/J 


l.a(THE,OCrAWE,) 


2:3(THE/nFTH) 
4:7(5U6MINOfc7«l^ 


5Y  &RAMANTL 


by  the  ratio  4:7,  though 
included  among  the  dis- 
sonances, forms,  accord- 
ing to  Helmholtz,  a  more 
perfect  consonance  with 
the  tonic  than  the  minor 
sixth. 

A  natural  deduction 
from  these  facts  is  that 
relations  of  architectural 
length  and  breadth, 
heighth  and  width,  to  be 
"musical"  should  be  cap- 
able of  being  expressed 
by  ratios  of  quantitively 
small  numbers,  prefer- 
ably an  odd  number  and 
an  even.  Although,  gen- 
erally speaking,  the  sim- 
pler the  ratio  the  more 
perfect  the  consonance, 
yet  the  intervals  of  the 
fifth  and  major  third 
(2:3  and  4:5),  are  con- 
sidered to  be  more  pleasing  than  the  octave  (1:2),  which  is  too  obviously 
a  repetition  of  the  original  note.  From  this  it  is  reasonable  to  assume  (and 
the  assumption  is  borne  out  by  experience),  that  proportions  the  numerical 
ratios  of  which  the  eye  resolves  too  readily  become  at  last  wearisome.  The 
relation  should  be  felt  rather  than  fathomed.  There  should  be  a  perception 
of  identity,  and  also  of  difference.  As  in  music,  where  dissonances  are 
introduced,  to  give  value  to  consonances  which  follow  them,  so  in  archi- 
tecture simple  ratios  should  be  employed  in  connection  with  those  more 
complex. 

Harmonics  are  those  tones  which  sound  with  and  re-enforce  any  musical 
note  when  it  is  sounded.  The  distinguishable  harmonics  of  the  tonic  yield 
the  ratios  i  :2,  2 13,  3  4,  4 15  and  4  7.  A  note  and  its  harmonics  form  a 
natural  chord.    They  may  be  compared  to  the  widening  circles  which  appear 


i-.2(th&  octave) 
4:7$ubminc*.7ik) 


i.z(the.ociave.) 

2.:3(THt  FIPTH) 
4-^CrHE  THIRD) 


PALAZZO  nSjRO. 


OOORj  IN  ^.  LORjtNZO 
IN  nAMA5CO.---EClME^ 


89 


THE  BEAUTIFUL  NECESSITY 


VII 


3l£NA 


CHAPEL  O^   THE 
PALAZZO  PUBUOO 

"THS  ^UBMIJSrORj  SEVENTH 


in  still  water  when  a  stone  is  dropped  into 
it,  for  when  a  musical  sound  disturbs  the 
quietude  of  that  pool  of  silence  which  we 
call  the  air,  it  ripples  into  overtones,  which, 
becoming  fainter  and  fainter,  die  away  into 
silence.  It  would  seem  reasonable  to  assume 
that  the  combination  of  numbers  which  ex- 
press these  overtones,  if  translated  into  terms 
of  space,  would  yield  proportions  agreeable 
to  the  eye,  and  such  is  the  fact,  as  the  accom- 
panying examples  sufficiently  indicate  (Illus- 
trations 88-91). 

The  interval  of  the  sub-minor  seventh 
(4:7),  used  in  this  way,  in  connection  with 
the  simpler  intervals  of  the  octave  (1:2),  and 
the  fifth  (2:3),  is  particularly  pleasing  be- 
cause it  is  neither  too  obvious  nor  too  subtle. 
This  ratio  of  4:7  is  important  for  the  reason 
that  it  expresses  the  angle  of  sixty  degrees, 
that  is,  the  numbers  4  and  7  represent  (very 
nearly)  the  ratio  between  one-half  the  base 
and  the  altitude  of  an  equilateral  triangle ; 
also  because  they  form  part  of  the  numerical 
series  i,  4,  7,  10,  etc.  Both  are  "mystic" 
numbers,  and  in  Gothic  architecture,  particu- 
larly, proportions  were  frequently  determined 
by  numbers  to  which  a  mystic  value  was  at- 
tached. According  to  Gwilt,  the  Gothic 
chapels  of  Windsor  and  Oxford  are  divided 
longitudinally  by  four,  and  transversely  by 
seven  equal  parts.  The  arcade  above  the 
roses  in  the  fagade  of  the  cathedral  of  Tours 

shows  seven  principal  units  across  the  front  of  the  nave,  and  four  in  each 

of  the  towers. 

A  distinguishing  characteristic  of  the  series  of  ratios  which  represent 

the  consonant  intervals  within  the  compass  of  an  octave  is  that  it  advances 

by  the  addition  of  i  to  both  terms :    r:2,  2  :^,  3 14,  4 15,  and  5  :6.     Such  a 


HOUSE  IN  KOME 


90 


VII 


FROZEN  MUSIC 


89 


series    always    approaches    unity,    just    as, 

represented  graphically  by  means  of  paral- 
lelograms, it  tends  towards  a  square.  Ac- 
cording to  W.  Watkins  Lloyd — in  an  article 

published  in   The   American   Architect   of 

March  31,  1888 — the  scale  of  ratios  which 

determined  all  the  important  proportions  of 

the  Parthenon  is  of  this  order,  advancing 

by  consecutive  differences  of  5.    The  author 

has  tio  means  of  verifying  the  truth  of  this 

statement,  but  gives  it  here  for  what  it  is 

worth  (Illustration  92).    Alberti  in  his  book 

presents  a  design  for  a  tower  showing  his 

idea  for  its  general  proportions.    It  consists 

of  six  stories,  in  a  sequence  of  orders.    The 

lowest  story  is  a  perfect  cube  and  each  of 

the  other  stories  is  11-12  of  the  story  below, 

or  diminishing  practically  in  the  proportion 

of  8,  7,  6,  5,  4,  3,  allowing  in  each  case  for 

the  amount  hidden  by  the  projection  of  the 

cornice  below ;  each  order  being  accurate  as 

regards  column,  entablature,  etc.     It  is  of 

interest  to  compare  this  with  Ruskin's  idea 

in  his  "Seven  Lamps,"  where  he  takes  the 

case  of  a  plant  called  Alisma  Plantago,  in 

which  the  various  branches  diminish  in  the  proportion  of  7,  6,  5,  4,  3,  respec- 
tively, and  so  carry  out  the  same  idea;  on  which  Ruskin  observes  that 

diminution  in  a  building  should  be  after  the  manner  of  Nature. 

It  would  be  a  profitless 
task  to  formulate  exact  rules 
of  architectural  proportion 
based  upon  the  laws  of 
musical  harmony.  The  two 
arts  are  too  different  from 
each  other  for  that,  and 
moreover  the  last  appeal 
must  always  be  to  the  eye, 


j:e= 

MINOR,  THIiCD-' 

lo-.ir 
8:13 

•*a-= 

MAJOR,  3EJ>' 

a-.4= 

FOUE,T)r' 

7:12 
6:11 

2:3 -= 
i-zcx 

SAO 

0:8 
2:7 

1  :6 

ORAPHICAl,  EXPRESSION 
OFMU5ICAL  INTE-RVAU. 


SCALL  SHOWING  PRJNCIRi\L  PEO- 
PORTIONS  OF  THE  PARTHENON— 


» 


90 


THE  BEAUTIFUL  NECESSITY 


VII 


THE.  PALAZZO  VBR,ZI  AT  VLRONA  (LOWLR.  PORTION 
ONLY}.  A  COMPOSITION  FOUND£.D  ON  THE  LQUAL  AND 
SECULAR.  DIVISION  OF  SPACL,  A$  MU5IG  IS  FOUNDED 
ON  THL  EQUAL  AND  R.LGULAR>  DIVISION  OF  TIM&--— 


93 


'ARCH1TEGTUR.E/  AS  RHYTTiM  a  division 

OF  SPACE/  COR-RjE-SPONDINO  TO  ^  AND  4/4  TIME*' 


and  not  to  a  mathemati- 
cal formula,  just  as  in 
music  the  last  appeal  is 
to  the  ear.  Laws  there 
are,  but  they  discover 
themselves  to  the  artist 
as  he  proceeds,  and  are 
for  the  most  part  incom- 
municable. Rules  and 
formulas  are  useful  and 
valuable  not  as  a  substi- 
tute for  inspiration,  but 
as  a  guide :  not  as  wings, 
but  as  a  tail.  In  this 
connection  perhaps  all 
that  is  necessary  for  the 
architectural  designer  to 
bear  in  mind  is  that  im- 
portant ratios  of  length 
^  and  breadth,  height  and 

and  width,  to  be  "musical"  should  be  expressed  by  quantitatively  small 
numbers,  and  that  if  possible  they  should  obey  some  simple  law  of  numerical 


^rf- 


r-r 


'-Tf 


fei  r  r  r  rl  r=F=^  rrri^^rrrr  ^^ 


VII 


FROZEN  MUSIC 


91 


arjchit£)cture  as  rhythm 

A  DIVISION  OF  SPACE .  OORRESPONDINer  TO 
^4 TIME.  THE  FRINGIPAL  AND  SUfiOEDlNAlE 
ACCENTS  RULINQ  ON  SK3NIKIQANT  FEATUKES 


PALAZZO  QiEAUD,  RQME--TCev10ST  SUCSY 


progression.  From  this  basic 
simplicity  complexity  will  follow, 
but  it  will  be  an  ordered  and 
harmonious  complexity,  like  that 
of  a  tree,  or  of  a  symphony. 

In  the  same  way  that  a  musical 
composition  implies  the  division 
of  time  into  equal  and  regular 
beats,  so  a  work  of  architecture 
should  have  for  its  basis  some 
unit  of  space.  This  unit  should 
be  nowhere  too  obvious  and  may 
be  varied  within  certain  limits, 
just  as  musical  time  is  retarded 
or  accelerated.  The  underlying 
rhythm  and  symmetry  will  thus 
give  value  and  distinction  to  such 
variation.  Vasari  tells  how 
Brunelleschi,  Bramante  and 
Leonardo  da  Vinci  used  to  work 
on  paper  ruled  in  squares, 
describing  it  as  a  "truly  ingenious  thing,  and  of  great  utility  in  the  work 
of  design."  By  this  means  they  developed  proportions  according  to  a  definite 
scheme.  They  set  to  work  with  a  division  of  space  analogous  to  the  musician's 
division  of  time.  The  examples  given  herewith  indicate  how  close  a  parallel 
may  exist  between  music  and  architecture  in  this  matter  of  ryhthm  (Illus- 
trations 93-95). 

It  is  a  demonstrable  fact  that  musical  sounds  weave  invisible  patterns 
in  the  air.  Architecture,  correspondingly,  in  one  of  its  aspects,  is  geometric 
pattern  made  fixed  and  enduring.  What  could  be  more  essentially  musical, 
for  example,  than  the  sea  arcade  of  the  Venetian  Ducal  Palace?  The  sand 
forms  traced  by  sound-waves  on  a  musically  vibrating  steel  plate  might  easily 
suggest  architectural  ornament  did  not  the  differences  of  scale  and  of  material 
tend  to  confuse  the  mind.  The  architect  should  occupy  himself  with 
identities,  not  differences.  If  he  will  but  bear  in  mind  that  architecture  is 
pattern  in  space,  just  as  music  is  pattern  in  time,  he  will  come  to  perceive  the 
essential  identity  between,  say  a  Greek  rosette  and  a  Gothic  rose-window; 


OOSJSIIGE  OP  THE  VIUAIA£2^SINA---^£QMB 


95 


92 


THE  BEAUTIFUL  NECESSITY 


VII 


an  arcade  and  an  egg  and  dart  moulding  (Illustration  96).  All  architectural 
forms  and  arrangements  which  give  enduring  pleasure  are  in  their  essence 
musical.  Every  well  composed  f agade  makes  harmony  in  three  dimensions ; 
every  good  roof  line  sings  a  melody  against  the  sky. 


ARCHrTECTURE;  AS  PATrER.N,CNo  scall) 


W\r^S^ 


OEiRLK--  FRjCMTHL 
ER£CHTHHCN  AT 
ATHEN5 


ITAL/IAN  GOTHIC  ~FRDM.  THL 
DUCAL.  PALACE.  AT  VENICE. 


OOTHIC^  FACADE 
OB  NOTRE  DAJViE/ 


ITALIAN  RE'NAI^SANCE/'^THE 
PALAZZO  5TOPPIANI  AT  TJCML 


96 


CONCLUSION 

IN  taking  leave  of  the  reader  at  the  end  of  this  excursion  together  among 
the  by-ways  of  a  beautiful  art,  the  author  must  needs  add  a  final  word  or 
two  touching  upon  the  purpose  and  scope  of  these  essays.  Architecture 
(like  everything  else)  has  two  aspects :  it  may  be  viewed  from  the  standpoint 
of  utility,  that  is,  as  construction :  or  from  the  standpoint  of  expressiveness, 
that  is,  as  decoration.  No  attempt  has  been  made  here  to  deal  with  its  first 
aspect,  and  of  the  second  (which  is  again  two-fold)  only  the  universal,  not 
the  particular  expressiveness  has  been  sought.  The  literature  of  architecture 
is  rich  in  works  dealing  with  the  utilitarian  and  constructive  side  of  the  art : 
indeed,  it  may  be  said  that  to  this  side  that  literature  is  almost  exclusively 
devoted.  This  being  so,  it  has  seemed  worth  while  to  attempt  to  show  the 
obverse  of  the  medal,  even  though  it  be  "tails"  instead  of  "heads." 

One  possible  criticism  the  author  meets,  not  with  apologies,  but  with 
defiance.  The  inductive  method  has  not,  in  these  pages,  been  honored  by 
a  due  observance.  It  would  have  been  easy  to  have  treated  the  subject 
inductively,  amassing  facts  and  drawing  conclusions,  but  to  have  done  so 
the  author  would  have  been  false  to  the  very  principle  about  which  the  work 
came  into  being.  With  the  acceptance  of  the  Ancient  Wisdom,  the  inductive 
method  becomes  a  thing  of  the  past.  Facts  are  no  longer  useful  in  order  to 
establish  a  hypothesis,  they  are  used  rather  to  elucidate  a  known  and  accepted 
truth ;  and  when  theosophy  shall  have  become  the  universal  religion  of 
mankind,  this  work,  if  it  survives  at  all,  will  be  chiefly,  perhaps  solely, 
remarkable  by  reason  of  the  fact  that  it  was  among  the  first  in  which  the 
attempt  was  made  to  again  unify  science,  art,  and  religion,  as  they  were 
unified  in  those  ancient  times  and  among  those  ancient  peoples  when  the 
Wisdom  swayed  the  hearts  and  minds  of  men. 

[93] 


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